# TNPSC Group 2A 2017 Answerkeys, Result Date Latest News Updates. Group 2

## TNPSC Group 2A 2017 Answerkeys, Result Date Latest News Updates

TNPSC Group 2A Exam 2017 notification was published by Tamil Nadu Public Service Commission on 27th April 2017. This time, the TNPSC has given a big surprise to all Group 2A Exam Aspirants with increase in the number of vacancies. In its Annual Planner, the Tamil Nadu Public Service Commission has informed that the tentative vacancies in the Group 2A 2017 will be 682. But in the official Group 2A notification, the number of vacancies was 1953. It was about three times more than the number mentioned in the annual planner . So, any candidate with very sincere preparation can surely get a job in upcoming TNPSC Group 2A 2017 Exam itself. All the best ! Important Dates in Group 2A Non Interview Exam 2017Group 2A 2017 Notification Date : 27-04-2017 Date of Exam :06-08-2017Last Date to Apply Online : 26-05-2017Last Date to pay fee offline : 29-05-2017

26-04-2017 : TNPSC Group 2A ( 24.01.2016) Exam Second Phase Counselling list published in the TNPSC Website. The Counselling is scheduled to be conducted from 15.05.2017 to 17.05.2017 at Tamil Nadu Public Service Commission Office, Chennai.

TNPSC Group 2A Counselling Candidates List

http://www.tnpsc.gov.in/results/sel_couns_ii_g2a2015.pdf

Group Two Non Interview Posts Exam 2017 Important Dates in Annual Planner 2016-17

According to the Annual Planner 2016 - 2017 available in the Tamilnadu Public Service Commission's Website, the TNPSC Group 2A Exam 2017 Notification was tentatively scheduled to be published in the first week of November 2016. The exam date for TNPSC Group 2A Examination 2017 was scheduled to be conducted in the month of February 2017. But the official notification is not published yet by the Tamil Nadu Public Service Commission .Counselling |

(Group 2A - NON-INTERVIEW POST) | CV: 3rd week of May, 2017 | 1st week of June,2017 |

03-11-2016 : TNPSC Group 2A 2016 First Phase Counselling -Candidates List Published at TNPSC Official Website - Check Soon. The list of register numbers of candidates who have been provisionally called for the first phase of Group 2A counselling is published in the TNPSC Official Website http://www.tnpsc.gov.in/results.html

The Group 2A Non Interview Posts Exam 2016 Counselling is scheduled to be held from 21-11-2016 to 02-12-2016 at TNPSC Office, Chennai - 600003.

TNPSC Group 2A 2016 Latest News UpdatesGroup 2A Certification Verification Schedule Published at TNPSC Website

TNPSC Group 2A Selected Candidates List for CV can be downloaded from the TNPSC Group 2A Result Websitehttp://www.tnpsc.gov.in/results.html TNPSC Group 2A (Non Interview Posts) Exam Certificate Verification started on Fourth July 2016.TNPSC Group 2A Counselling Schedule for Assistant posts

http://www.tnpsc.gov.in/vacs/g2a2015_COUNSELLING%20SCHEDULE.pdf

Counselling schedule for Group 2A Personal Clerk posts

http://www.tnpsc.gov.in/vacs/COUNSELLING%20SCHEDULE_pc.pdf

The TNPSC Group 2A Non Interview Posts Exam Certificate Verification is scheduled to be conducted from 4th July 2016 to 19th July 2016.

--------------------------------------------

TNPSC Group 2A Result Published Check Soon

http://tnpsc.gov.in/results.html

Check your Marks and Communal and over all ranks of Group 2A Exam from the below link

http://tnpsc.gov.in/ResultGet-g2a2015rank.html

TNPSC Group 2A Examination First Phase Certificate Verification for the selected candidates is expected to be conducted from 4th July 2016. All the best for the candidates who get chance in the first phase of Certificate Verification ! All the best for other Candidates to perform successfully in upcoming TNPSC Exams this year !

06-06-2016 : TNPSC Group 2A Non Interview Exam Result to be published soon - TNPSC Chairman Informed. In an interview to the media persons, the Chairman has informed the results of Group 1 , 2 and VAO Exams will be published soon.

TNPSC Group 2A 2016 Vacancies - Detailed List for various posts are published in the TNPSC Official Website www.tnpsc.gov.in.http://www.tnpsc.gov.in/vacs/g2a_2016_dist_of_vacs.pdf

02-06-2016 : TNPSC GROUP-IIA 29-06-2014 Exam Certificate Verification Phase IV and Counselling Phase V called for. List of Candidates for the certificate verification and counselling is published in the following websitehttp://tnpsc.gov.in/results.htmlTNPSC Group 2A 2016 Result date is tentatively scheduled to be published in the Month of April 2016. Source : TNPSC Annual Planner 2016 -2017Counselling |

CCSE - IIA (TNPSC GROUP 2A) (NON-INTERVIEW POST) (VACANCIES: 1947) | 4th week of June 2016 |

Official Website for TNPSC Group 2A Results

07-04-2016 : TNPSC Group 2A (Exam Date 29.06.2014) Counselling Announced for Fourth Phase (IV Phase)

TNPSC Group 2A Certificate Verification Dates

Group 2A Assistant and Personal Clerk Posts - 12.04.2016

Group 2A Non Interview Posts Counselling Dates

Group Two Non Interview - Assistant Posts and Personal Clerk - 13.04.2016

To know your rank position in the Group 2A Exam 2014 visit http://www.tnpsc.gov.in/ResultGet-G2A2014.html

To know department wise vacancy position and counselling schedule of TNPSC Group II A Posts visithttp://www.tnpsc.gov.in/g2a2014_counselling.html

Download TNPSC Group 2A 2016 Exam Official Answerkey from TNPSC Website

http://www.tnpsc.gov.in/answerkeys_24_01_2016.html

TNPSC Group 2A Expected Cut Off Marks

------------TNPSC VAO 2016 Cut off marks (Expected)

TNPSC Group 2A 24-01-2016 Answer Key

TNPSC Group 2A January 2016 Exam Hall Ticket is published in the TNPSC official website and ready to be downloaded now. You can download and print the Group Two Non Interview Postings Exam 2015 Hall ticket from TNPSC Official Website www.tnpscexams.net. If your Group Two Non Interview Posts Exam January 2016 hall ticket / admit card is not available in the TNPSC website, please check the same in the rejection list of candidates published in the TNPSC website. If your TNPSC Group Two Non Interview Posts 2016 Exam application details is not available in the rejection list published in the TNPSC Website also, you can contact TNPSC office with required documents to recover your hall tickets soon. All the best for your success in the upcoming TNPSC Group 2A Exam 2016!

TNPSC Group Two 2016 Hall Ticket Download Link

http://tnpscexams.net/

Direct Link to download Gr 2A Non Interview Hall Ticket

http://182.18.164.63/tnpscadmitcard17/frmLogin172015.aspx15-01-2016 : 8.5 lakhs candidates applied for 1947 TNPSC Group Two Non Interview Posts Examination 2016. Now the Tamil Nadu Public Service Commission has published the TNPSC Group Two Non Interview Posts Exam 2016 Hall Ticket in the www.tnpscexams.net website. You can download the Group 2A Hall Ticket from the TNPSC official website www.tnpsc.gov.in . If your Group Two Non Interview Exam Call Letter is not found in the rejection list published in the TNPSC Website, you can contact the TNPSC office with sufficient documents through [email protected]

TNPSC Group 2A Latest News Source : Dinamalar, 15-01-2016

http://www.dinamalar.com/news_detail.asp?id=1434223&Print=1

24-11-2015 : Eight Lakhs Total Candidates applied for 1,947 Group Two Non Interview Posts - TNPSC Group Two Non Interview Exam 2015 was applied by more than Eight Lakh Graduates through out Tamilnadu. Source : The Hindu Tamil News Paper Today(24-11-2015).So the competition in the Group Two Non Interview Post Exam 2015 is expected to be tough this time, prepare yourself to face the tough competition in the Group Two Non Interview Exam . All the best !

In the TNPSC Group 2A 2015 Notification, the last date for applying Group Two Non Interview Exam online was mentioned as 11-11-2015. Now the TNPSC has Changed the last date to apply online for the Group Two Non Interview posts exam to 18-11-2015. The last date to pay fee in offline mode (through Bank or Post Office) is also postponed to 20-11-2015. If you have not applied for the Group 2A Exam 2015 yet, apply online from www.tnpscexams.net website soon.

TNPSC Group Two Non Interview Exam Online Application Website

http://tnpscexams.net/

Important News !!! TNPSC Group 2A Exam Date is changed to 24th January 2016.The Group 2A Non Interview Posts Exam 2015 was scheduled to be conducted on 27th December 2015 . Now the Tamilnadu Public Service Commission haspostponed the Group 2A Exam date to 24th January 2016. TNPSC has informed that the candidates who have already successfully applied for the TNPSC Group 2A exam 2015 need not apply again for the 24-01-2016 examination.

Note : Last date for applying TNPSC Group 2A 2015 Examination Online will be 18th November 2015. If you have not applied for the TNPSC Group 2A Exam 2015, please apply the Group IIA Exam January 2016 soon before 18-11-2015, the last date to apply. All the best !

Newly added posts in Group 2A Supplementary Notification Details ( Total 84 posts)

TNPSC Group 2A Supplement Notification for 84 posts Published on 20-10-2015

84 additional posts added . Now total number of TNPSC Group 2A 2015 posts became 1947. Below is the list of additionally added vacancies in the TNPSC Group Two Non Interview Exam 2015 through the supplement notification published in the TNPSC Website.

1. Assistant post in Tamilnadu Forest Department - 36 posts

2.Assistant in Stationery and Printing Department - 30 posts

3. Assistant in Survey and Settlement Department - 10 posts

4.Personal Clerk in Secretariat (Other than Law and Finance Department) - 6 ST + 1 MBC/DC (Deaf)

5.Personal Clerk in Tamil Nadu Public Service Commission - 1 BC Muslim(BCM) Category

The most awaited TNPSC Group 2A Exam Notification is Announced by TNPSC. The Official notification advertisement is published in the Dinathanthi Newspaper Today, Page No. 9. and in the TNPSC's Official website www.tnpsc.gov.in also. The TNPSC Group Two Non Interview Posts Exam 2015 (Group 2A) Exam Announcement has total 1863 vacancies. The vacancies include various posts in 32 government departments like Civil Supplies, Commercial Dept, Jail, Transport, Registration Department and other departments. Among the total number of posts, Engineering candidates can apply for about 1524 posts only.

Important Dates for TNPSC Group 2A 2015 Examination

Group 2A Exam Date : 27-12-2015 (10AM to 1PM)

Last Date to Apply Online : 11-11-2015

TNPSC Official Website for TNPSC Group 2A 2015 -2016 Notification

http://www.tnpsc.gov.in/latest-notification.html

TNPSC Group 2A Result Date Latest News

Total Number of Vacancies : 1863. The TNPSC Group 2A 2014 Vacancies include Personal Clerk, Assistants, Planning Junior Assistant, Lower Division Clerk, Junior Co-operative Auditor in various departments under Tamilnadu Government.

How many TNPSC Group 2A posts Applicable for Engineering Graduates in the Group 2 Non Interview Posts 2015 Notification?All any degree qualification posts in the TNPSC Group 2A Exam 2016 can be applied by all Engineering candidates who have completed the degree with out arrears. The Group 2A 2015 notification has 1524 posts in any Degree Qualification Category. So, dear engineering candidates, if you study hard with a plan, surely you will get a job in this year Group Two Non Interview Exam 2016 itself. All the best for your success !

List of Group 2A Assistants posts for which Engineering Graduates are eligible to applyName of the Group 2A Post | |||

Commissioner of Revenue Administration | |||

Medical and Rural Health Services | |||

Rural Development Punchayat Raj | |||

Vigilance and Anti corruption | |||

Urban Land Ceiling and Land Tax Dept | |||

Commissioner of Commercial Tax | |||

Commercial Tax, Chennai (South) | |||

Commercial Tax, Trichy Division | |||

Commercial Tax, Salem Division | |||

Commercial Tax, Vellore Division | |||

Commercial Tax, Coimbatore Division | |||

Commercial Tax, Madurai Division | |||

Commercial Tax, Tiruelveli Division | |||

TNPSC Group 2A Posts Age Limit ( Age Limit as on 1st July )

Minimum Age Limit to apply TNPSC Group 2A Exam - 18 Years Maximum Age Limit for applying TNPSC Group 2A Exam- SC/SCA/ST/BC/BCM/MBC - No Maximum Age Limit
- Others than SC/SCA/ST/BC/MBC - 30 Years

- General Studies (Degree Standard) - 75 Questions
- Aptitude and Mental Ability Test (SSLC Standard) - 25 Questions
- General Tamil / General English (SSLC Standard) - 100 Questions

Download TNPSC Group 2A Exam Latest Revised Syllabus from TNPSC official website

(TNPSC Group 2A Syllabus is given in the Page Number 54 - 64)

For all latest news updates regarding TNPSC Group 2A 2016 Result date, be connected with us.

Share your thoughts/experience/queries about the TNPSC Group 2A Exam in the comment section below.

For TNPSC Official Website Visitwww.tnpsc.gov.inwww.tnpscportal.in

## 2-group - Wikipedia

This article is about 2-dimensional higher groups. For 2-primary groups (groups of order 2p), see p-primary group.In mathematics, a 2-group, or 2-dimensional higher group, is a certain combination of group and groupoid. The 2-groups are part of a larger hierarchy of n-groups. In some of the literature, 2-groups are also called gr-categories or groupal groupoids.

### Definition[edit]

A 2-group is a monoidal category G in which every morphism is invertible and every object has a weak inverse. (Here, a weak inverse of an object x is an object y such that xy and yx are both isomorphic to the unit object.)

### Strict 2-groups[edit]

Much of the literature focuses on strict 2-groups. A strict 2-group is a strict monoidal category in which every morphism is invertible and every object has a strict inverse (so that xy and yx are actually equal to the unit object).

A strict 2-group is a group object in a category of categories; as such, they are also called groupal categories. Conversely, a strict 2-group is a category object in the category of groups; as such, they are also called categorical groups. They can also be identified with crossed modules, and are most often studied in that form. Thus, 2-groups in general can be seen as a weakening of crossed modules.

Every 2-group is equivalent to a strict 2-group, although this can't be done coherently: it doesn't extend to 2-group homomorphisms.

### Properties[edit]

Weak inverses can always be assigned coherently: one can define a functor on any 2-group G that assigns a weak inverse to each object and makes that object an adjoint equivalence in the monoidal category G.

Given a bicategory B and an object x of B, there is an automorphism 2-group of x in B, written AutB(x). The objects are the automorphisms of x, with multiplication given by composition, and the morphisms are the invertible 2-morphisms between these. If B is a 2-groupoid (so all objects and morphisms are weakly invertible) and x is its only object, then AutB(x) is the only data left in B. Thus, 2-groups may be identified with one-object 2-groupoids, much as groups may be identified with one-object groupoids and monoidal categories may be identified with one-object bicategories.

If G is a strict 2-group, then the objects of G form a group, called the underlying group of G and written G0. This will not work for arbitrary 2-groups; however, if one identifies isomorphic objects, then the equivalence classes form a group, called the fundamental group of G and written π1(G). (Note that even for a strict 2-group, the fundamental group will only be a quotient group of the underlying group.)

As a monoidal category, any 2-group G has a unit object IG. The automorphism group of IG is an abelian group by the Eckmann–Hilton argument, written Aut(IG) or π2(G).

The fundamental group of G acts on either side of π2(G), and the associator of G (as a monoidal category) defines an element of the cohomology group h4(π1(G),π2(G)). In fact, 2-groups are classified in this way: given a group π1, an abelian group π2, a group action of π1 on π2, and an element of h4(π1,π2), there is a unique (up to equivalence) 2-group G with π1(G) isomorphic to π1, π2(G) isomorphic to π2, and the other data corresponding.

The element of h4(π1,π2) associated to a 2-group is sometimes called its Sinh invariant, as it was developed by Grothendieck's student Hoàng Xuân Sính.

### Fundamental 2-group[edit]

Given a topological space X and a point x in that space, there is a fundamental 2-group of X at x, written Π2(X,x). As a monoidal category, the objects are loops at x, with multiplication given by concatenation, and the morphisms are basepoint-preserving homotopies between loops, with these morphisms identified if they are themselves homotopic.

Conversely, given any 2-group G, one can find a unique (up to weak homotopy equivalence) pointed connected space (X,x) whose fundamental 2-group is G and whose homotopy groups πn are trivial for n > 2. In this way, 2-groups classify pointed connected weak homotopy 2-types. This is a generalisation of the construction of Eilenberg–Mac Lane spaces.

If X is a topological space with basepoint x, then the fundamental group of X at x is the same as the fundamental group of the fundamental 2-group of X at x; that is,

π1(X,x)=π1(Π2(X,x)).{\displaystyle \pi _{1}(X,x)=\pi _{1}(\Pi _{2}(X,x)).\!}This fact is the origin of the term "fundamental" in both of its 2-group instances.

Similarly,

π2(X,x)=π2(Π2(X,x)).{\displaystyle \pi _{2}(X,x)=\pi _{2}(\Pi _{2}(X,x)).\!}Thus, both the first and second homotopy groups of a space are contained within its fundamental 2-group. As this 2-group also defines an action of π1(X,x) on π2(X,x) and an element of the cohomology group h4(π1(X,x),π2(X,x)), this is precisely the data needed to form the Postnikov tower of X if X is a pointed connected homotopy 2-type.

### References[edit]

- John C. Baez and Aaron D. Lauda, Higher-dimensional algebra V: 2-groups, Theory and Applications of Categories 12 (2004), 423–491.
- John C. Baez and Danny Stevenson, The classifying space of a topological 2-group.
- R. Brown and P.J. Higgins, The classifying space of a crossed complex, Math. Proc. Camb. Phil. Soc. 110 (1991) 95-120.
- R. Brown, P.J. Higgins, R. Sivera, Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids, EMS Tracts in Mathematics Vol. 15, 703 pages. (2011).
- Hendryk Pfeiffer, 2-Groups, trialgebras and their Hopf categories of representations, Adv. Math. 212 No. 1 (2007) 62–108.
- Hoàng Xuân Sính, Gr-catégories, thesis, 1975.

### External links[edit]

en.wikipedia.org

## Trends in Group 2 Elements Chemistry Tutorial

### Trends in Electronic Configuration of Group 2 Elements

Consider the electronic configuration of group 2 elements. Can you see a trend (a pattern)?

name electronic configurationberyllium | 2,2 |

magnesium | 2,8,2 |

calcium | 2,8,8,2 |

strontium | 2,8,18,8,2 |

barium | 2,8,18,18,8,2 |

radium | 2,8,18,32,18,8,2 |

Atoms of group 2 elements have just 2 electrons in the highest energy level (also known as the valence shell of electrons).

It is even easier to see this if we use a short-hand description of the electronic configuration of each atom in which the electrons that make up part of a Noble Gas (group 18) electron configuration are represented in square brackets followed by the number of electrons in the valence shell. We have done this in the table below:

name short-hand electronic configurationberyllium | [He],2 |

magnesium | [Ne],2 |

calcium | [Ar],2 |

strontium | [Kr],2 |

barium | [Xe],2 |

radium | [Rn],2 |

If an atom (M) of a group 2 element lost both these valence electrons (2e-), then the ion of the group 2 element would have a charge of +2 (M2+) as shown in the equations below:

General equation: examples:M | → | M2+ | + | 2e- |

Be | → | Be2+ | + | 2e- |

Mg | → | Mg2+ | + | 2e- |

Ca | → | Ca2+ | + | 2e- |

Ba | → | Ba2+ | + | 2e- |

Sr | → | Sr2+ | + | 2e- |

Ra | → | Ra2+ | + | 2e- |

And, the positively charged ion (cation) formed would have the same electronic configuration as a group 18 (Noble Gas) element, we say that the cation is isoelectronic with the Noble Gas, as shown below:

cation electronic configurationBe2+ | [He] |

Mg2+ | [Ne] |

Ca2+ | [Ar] |

Sr2+ | [Kr] |

Ba2+ | [Xe] |

Ra2+ | [Rn] |

and the cation of a group 2 element would therefore be chemically very stable (that is, no longer very reactive), just like a Noble Gas (group 18 element).

So, just how likely is it that a group 2 element will lose both valence electrons and form a cation .....

### Trends in Ionisation Energy of Group 2 Elements

Ionisation energy (or ionization energy) is the energy required to remove an electron from a gaseous species.

First ionisation energy (or first ionization energy) refers to the energy required to remove an electron from a gaseous atom.

We can write a general equation to describe the removal of an electron (e-) from a gaseous atom (M(g)) to produce a gaseous cation with a charge of +1 (M+(g)) as:

M(g) → M+(g) + e-

Second ionisation energy refers to the energy required to remove an electron (e-) from the gaseous ion with a charge of +1 (M+(g)) to form a gaseous ion with a charge of +2 (M2+(g)) as shown in the equation below:

M+(g) → M2+(g) + e-

If the value of the ionisation energy is high, then lots of energy is required to remove the electron, and the reaction is less likely to occur readily. If the value of the ionisation energy is low, then little energy is required to remove the electron, and the reaction is more likely to occur readily.

So let's look at the values of the first and second ionisation energy for each Group 2 element (alkaline-earth metal):

1st Ionisation Reaction 1st Ionisation Energy (kJ mol-1) 2nd Ionisation Reaction 2nd Ionisation Energy (kJ mol-1)Be(g) | → | Be+(g) | + | e- | 899 | highest | Be+(g) | → | Be2+(g) | + | e- | 1757 | highest |

Mg(g) | → | Mg+(g) | + | e- | 738 | ↑ | Mg+(g) | → | Mg2+(g) | + | e- | 1450 | ↑ |

Ca(g) | → | Ca+(g) | + | e- | 590 | ↑ | Ca+(g) | → | Ca2+(g) | + | e- | 1145 | ↑ |

Sr(g) | → | Sr+(g) | + | e- | 549 | ↑ | Sr+(g) | → | Sr2+(g) | + | e- | 1064 | ↑ |

Ba(g) | → | Ba+(g) | + | e- | 503 | lowest | Ba+(g) | → | Ba2+(g) | + | e- | 965 | lowest |

As you go down group 2 from top to bottom, the value of first ionisation energy decreases, it is progressively easier to remove the first valence electron.

As you go down group 2 from top to bottom, the value of the second ionisation energy decreases, it is progressively easier to remove the second valence electron.

The suggestion here is that the chemical reactivity of the elements increase as you go down group 2 from top to bottom. That is, since it requires less energy to remove the two valence electrons as you go down the group, the chemical activity of these elements will increase going down the group.

You might also notice that the value of the second ionisation energy for each element is about double that of the first ionisation energy.

If we are right and the electronic configuration of a Noble gas (Group 18) element is particularly stable, then it should be very difficult, that is, require a lot more energy, to remove the third electron from each Group 2 element.

Third ionisation: M2+(g) → M3+(g) + e-

So, let's look at the value of each third ionization for each group 2 element:

name First Ionisation Energy (kJ mol-1 Second Ionisation Energy (kJ mol-1 Third Ionisation Energy (kJ mol-1beryllium | 899 | (× 1.95 =) | 1757 | (× 8.45 = ) | 14,849 |

magnesium | 738 | (× 1.96 = ) | 1450 | (× 5.33 = ) | 7730 |

calcium | 590 | (× 1.94 = ) | 1145 | (× 4.32 = ) | 4941 |

strontium | 549 | (× 1.94 = ) | 1064 | (× 3.95 = ) | 4207 |

barium | 503 | (× 1.92 = ) | 965 | (× 3.54 = ) | 3420 |

In general, it requires a bit less than twice as much energy to remove the second valence electron than it does to remove the first valence electron from a gaseous atom of each element.

But in general it requires more than double this amount of energy again in order to remove the third electron. This strongly supports the concept that the electronic configuration of a Noble Gas (group 18) element is remarkably stable and that any atom or ion with this structure will not be chemically reactive.

As a result, Group 2 elements form ionic compounds in which the group 2 cation has a charge of 2+. (5)

But why is it easier to remove these valence electrons as you go down group 2 from top to bottom....

### Trends in Atomic Radius of Group 2 Elements

First, lets think about the number of electron shells (or energy levels) being filled to make an atom of each group 2 element:

name electronic configuration Number of occupied energy levelsberyllium | 2,2 | 2 |

magnesium | 2,8,2 | 3 |

calcium | 2,8,8,2 | 4 |

strontium | 2,8,18,8,2 | 5 |

barium | 2,8,18,18,8,2 | 6 |

radium | 2,8,18,32,18,8,2 | 7 |

As you go down group 2 from top to bottom, you are adding a whole new "electron shell" to the electronic configuration of each atom. Surely that will increase the size of each atom as you go down the group? We record the "size" of an atom using its "atomic radius". Consider the values for the atomic radius of each of the atoms in group 2 as shown in the table below:

name atomic radius (pm) Trendberyllium | 112 | smallest |

magnesium | 160 | ↓ |

calcium | 197 | ↓ |

strontium | 215 | ↓ |

barium | 217 | largest |

As you go down group 2 from top to bottom the radius of the atom of each successive element increases. This means that the negatively charged valence electrons get further away from the positively charged nucleus and we say that these electron are 'shielded'. So, the positively charged nucleus has less of a "pull" on the valence electrons as you go down the group. Therefore, the valence electrons are easier to remove, and therefore the ionisation energy decreases down the group as discussed in the previous section.

All of this means that the reactivity of Group 2 elements increases as you go down the group from top to bottom...

### Trends in Reactivity of Group 2 Elements (alkaline-earth metals)

All the group 2 elements (M(s)), except beryllium, react with water (h3O(l)) to form hydrogen gas (h3(g)) and an alkaline (basic) aqueous solution (M(OH)2(aq)) as shown in the balanced chemical equations below:

Mg(s) | + | 2h3O(l) | → | h3(g) | + | Mg(OH)2(aq) |

Ca(s) | + | 2h3O(l) | → | h3(g) | + | Ca(OH)2(aq) |

Sr(s) | + | 2h3O(l) | → | h3(g) | + | Sr(OH)2(aq) |

Ba(s) | + | 2h3O(l) | → | h3(g) | + | Ba(OH)2(aq) |

The reaction between magnesium and water is usually slow because magnesium readily reacts with oxygen and a protective layer of magnesium oxide forms over the metal. The reactions between other Group 2 elements and water is vigorous.

Beryllium and magnesium do not combine directly with hydrogen, however, calcium, strontium and barium will combine directly with hydrogen:

Ca(s) | + | h3(g) | → | Cah3(s) |

Sr(s) | + | h3(g) | → | Srh3(s) |

Ba(s) | + | h3(g) | → | Bah3(s) |

Reactions with water and hydrogen as described above indicate that there is a general trend in the chemical reactivity of group 2 elements: the reactivity of the group 2 elements increases as you go down the group from top to bottom.

The group 2 metals (M(s)) react with oxygen gas (O2(g)) at room temperature and pressure to form oxides with the general formula MO as shown in the balanced chemical reactions below:

2Be(s) | + | O2(g) | → | 2BeO(s) |

2Mg(s) | + | O2(g) | → | 2MgO(s) |

2Ca(s) | + | O2(g) | → | 2CaO(s) |

2Sr(s) | + | O2(g) | → | 2SrO(s) |

2Ba(s) | + | O2(g) | → | 2BaO(s) |

Group 2 metals (M(s)) react with halogens (group 17 elements) to form halides with the formula MX2. For example, group 2 elements react with the halogen chlorine gas (Cl2(g)) to form an ionic chloride(6) (MCl2(s)) as shown in the balanced chemical equations below:

Be(s) | + | Cl2(g) | → | BeCl2(s) |

Mg(s) | + | Cl2(g) | → | MgCl2(s) |

Ca(s) | + | Cl2(g) | → | CaCl2(s) |

Sr(s) | + | Cl2(g) | → | SrCl2(s) |

Ba(s) | + | Cl2(g) | → | BaCl2(s) |

Group 2 elements will also combine with sulfur to form sulfides with the general formula MS:

Be(s) | + | S | → | BeS |

Mg(s) | + | S | → | MgS |

Ca(s) | + | S | → | CaS |

Sr(s) | + | S | → | SrS |

Ba(s) | + | S | → | BaS |

and they will combine with nitrogen to form nitrides with the general formula M3N2:

3Be(s) | + | N2(g) | → | Be3N2 |

3Mg(s) | + | N2(g) | → | Mg3N2 |

3Ca(s) | + | N2(g) | → | Ca3N2 |

3Sr(s) | + | N2(g) | → | Sr3N2 |

3Ba(s) | + | N2(g) | → | Ba3N2 |

www.ausetute.com.au

## Group a - Wikipedia

Look for Group a on one of Wikipedia's sister projects:Wiktionary (free dictionary) | |

Wikibooks (free textbooks) | |

Wikiquote (quotations) | |

Wikisource (free library) | |

Wikiversity (free learning resources) | |

Commons (images and media) | |

Wikivoyage (free travel guide) | |

Wikinews (free news source) | |

Wikidata (free linked database) |

- Log in or create an account to start the Group a article, alternatively use the Article Wizard, or add a request for it.
- Search for "Group a" in existing articles.
- Look for pages within Wikipedia that link to this title.

Other reasons this message may be displayed:

- If a page was recently created here, it may not be visible yet because of a delay in updating the database; wait a few minutes or try the purge function.
- Titles on Wikipedia are case sensitive except for the first character; please check alternative capitalizations and consider adding a redirect here to the correct title.
- If the page has been deleted, check the deletion log, and see Why was the page I created deleted?.

en.wikipedia.org

## Atomic and physical properties of Periodic Table Group 2

Trying to explain this

The only explanations you are likely to ever come across relate to the melting points. I will give you the most common explanation, and then explain why I think it is completely wrong!

The faulty explanation

All of these elements are held together by metallic bonds. The melting points get lower as you go down the Group because the metallic bonds get weaker. The oddity of magnesium has to be explained separately.

The atoms in a metal are held together by the attraction of the nuclei to the delocalised electrons. As the atoms get bigger, the nuclei get further away from these delocalised electrons, and so the attractions fall. That means that the atoms are more easily separated to make a liquid and finally a gas.

As you go down the Group, the arrangement of the atoms in the various solid metals changes. Beryllium and magnesium are both hexagonal close-packed; calcium and strontium are face-centred cubic; barium is body-centred cubic. Don't worry if you don't know what this means. All that matters is that there is a change in crystal structure between magnesium and calcium. That is supposed to account for the fact that magnesium is out of line with the rest of the Group.

Why I don't believe this explanation

The odd position of magnesium

Let's take this first, because that argument is relatively easy to demolish.

Despite the fact that the first four elements have two different structures, those structures are both 12-co-ordinated. Each atom is touched by 12 surrounding atoms. In that case, you would expect the metallic bond to be similar in each case, because the orbitals are going to overlap and delocalise in the same sort of way. Any differences just due to the structures should only be minor.

By contrast, barium is 8-co-ordinated (like the Group 1 metals). That's a less efficient packing, and you might expect that to be reflected in a much weaker metallic bond. Although the barium melting point is lower than that of strontium, it isn't dramatically lower. It just follows the general trend - suggesting that the major change of structure isn't making much difference. You can't have it both ways! If a minor change of structure at magnesium-calcium makes a huge difference, then a major one at barium should make an even bigger difference. It obviously doesn't.

The strength of the metallic bonds

Melting point isn't a good guide to the strength of the metallic bonds. When a metal melts, the bonds aren't completely broken - only loosened enough for the atoms to move around. Metallic bonds are still present in the molten metal, and aren't entirely broken until it boils.

That means that boiling point, or the size of the atomisation energy, is a much better guide to the real strengths of the metallic bonds. With both of those measures, you are ending up with free atoms in the gas state with the metallic bond completely broken.

Cotton and Wilkinson, in their classic degree level book Advanced Inorganic Chemistry say "The strength of binding between the atoms in metals can conveniently be measured by the energies of atomization of the metallic elements." (Third edition, page 68.)

If you look back at the atomisation energy chart above, you will see that magnesium still has the lowest value, but there is no obvious trend in atomisation energies as you go down the Group. The explanation about weaker metallic bonds as you go down the Group can't be accurate either.

If you look at figures for Group 1 rather than Group 2, then the trends for all the various measures (melting point, boiling point and atomisation energy) work almost perfectly as you go down the Group. There is obviously something happening in Group 2 which is causing the problem. I have no idea at all what it might be.

A final comment

I have had a request for solid information about this on Chemguide since 2002, during which time this page will have been read by hundreds of thousands, if not millions, of visitors. In all that time, nobody has suggested an explanation which would account for the low melting point value for magnesium, or the lack of any pattern with the other two properties.

If you can see flaws in what I have said above, please get in touch with me. I would also be grateful to anyone who could point me towards an explanation, even if it is too difficult to use at this level, or even too difficult for me to understand. But that explanation has to be capable of accounting for all the variations in the data.

There is one book that I have come across which is honest enough to admit the difficulty. A.G.Sharpe, in his degree level book Inorganic Chemistry admits that there is no easy explanation for the variations in the physical data in Group 2. If that is indeed the case, as looks pretty likely, it is a pity that anyone should encourage faulty explanations like the one above. Much better to have no explanation than a deeply flawed one.

www.chemguide.co.uk

## G2 (mathematics) - Wikipedia

In mathematics, G2 is the name of three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras g2{\displaystyle {\mathfrak {g}}_{2}}, as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups. G2 has rank 2 and dimension 14. It has two fundamental representations, with dimension 7 and 14.

The compact form of G2 can be described as the automorphism group of the octonion algebra or, equivalently, as the subgroup of SO(7) that preserves any chosen particular vector in its 8-dimensional real spinor representation.

### History[edit]

The Lie algebra g2{\displaystyle {\mathfrak {g}}_{2}}, being the smallest exceptional simple Lie algebra, was the first of these to be discovered in the attempt to classify simple Lie algebras. On May 23, 1887, Wilhelm Killing wrote a letter to Friedrich Engel saying that he had found a 14-dimensional simple Lie algebra, which we now call g2{\displaystyle {\mathfrak {g}}_{2}}.[1]

In 1893, Élie Cartan published a note describing an open set in C5{\displaystyle \mathbb {C} ^{5}} equipped with a 2-dimensional distribution—that is, a smoothly varying field of 2-dimensional subspaces of the tangent space—for which the Lie algebra g2{\displaystyle {\mathfrak {g}}_{2}} appears as the infinitesimal symmetries.[2] In the same year, in the same journal, Engel noticed the same thing. Later it was discovered that the 2-dimensional distribution is closely related to a ball rolling on another ball. The space of configurations of the rolling ball is 5-dimensional, with a 2-dimensional distribution that describes motions of the ball where it rolls without slipping or twisting.[3][4]

In 1900, Engel discovered that a generic antisymmetric trilinear form (or 3-form) on a 7-dimensional complex vector space is preserved by a group isomorphic to the complex form of G2.[5]

In 1908 Cartan mentioned that the automorphism group of the octonions is a 14-dimensional simple Lie group.[6] In 1914 he stated that this is the compact real form of G2.[7]

In older books and papers, G2 is sometimes denoted by E2.

### Real forms[edit]

There are 3 simple real Lie algebras associated with this root system:

- The underlying real Lie algebra of the complex Lie algebra G2 has dimension 28. It has complex conjugation as an outer automorphism and is simply connected. The maximal compact subgroup of its associated group is the compact form of G2.
- The Lie algebra of the compact form is 14-dimensional. The associated Lie group has no outer automorphisms, no center, and is simply connected and compact.
- The Lie algebra of the non-compact (split) form has dimension 14. The associated simple Lie group has fundamental group of order 2 and its outer automorphism group is the trivial group. Its maximal compact subgroup is SU(2) × SU(2)/(−1,−1). It has a non-algebraic double cover that is simply connected.

### Algebra[edit]

#### Dynkin diagram and Cartan matrix[edit]

The Dynkin diagram for G2 is given by .

Its Cartan matrix is:

[2−1−32]{\displaystyle \left[{\begin{smallmatrix}\;\,\,2&-1\\-3&\;\,\,2\end{smallmatrix}}\right]}#### Roots of G2[edit]

The 12 vector root system of G2 in 2 dimensions. | The A2Coxeter plane projection of the 12 vertices of the cuboctahedron contain the same 2D vector arrangement. | Graph of G2 as a subgroup of F4 and E8 projected into the Coxeter plane |

Although they span a 2-dimensional space, as drawn, it is much more symmetric to consider them as vectors in a 2-dimensional subspace of a three-dimensional space.

(1,−1,0), (−1,1,0) (1,0,−1), (−1,0,1) (0,1,−1), (0,−1,1) | (2,−1,−1), (−2,1,1) (1,−2,1), (−1,2,−1) (1,1,−2), (−1,−1,2) |

One set of simple roots, for is:

(0,1,−1), (1,−2,1)#### Weyl/Coxeter group[edit]

Its Weyl/Coxeter group G=W(G2){\displaystyle G=W(G_{2})} is the dihedral group, D6{\displaystyle D_{6}} of order 12. It has minimal faithful degree μ(G)=5{\displaystyle \mu (G)=5}.

#### Special holonomy[edit]

G2 is one of the possible special groups that can appear as the holonomy group of a Riemannian metric. The manifolds of G2 holonomy are also called G2-manifolds.

### Polynomial invariant[edit]

G2 is the automorphism group of the following two polynomials in 7 non-commutative variables.

C1=t2+u2+v2+w2+x2+y2+z2{\displaystyle C_{1}=t^{2}+u^{2}+v^{2}+w^{2}+x^{2}+y^{2}+z^{2}} C2=tuv+wtx+ywu+zyt+vzw+xvy+uxz{\displaystyle C_{2}=tuv+wtx+ywu+zyt+vzw+xvy+uxz} (± permutations)which comes from the octonion algebra. The variables must be non-commutative otherwise the second polynomial would be identically zero.

### Generators[edit]

Adding a representation of the 14 generators with coefficients A..N gives the matrix:

Aλ1+...+Nλ14=[0C−BE−D−GF−M−C0AF−G+ND−K−E−LB−A0−NML−K−E−FN0−A+H−B+IC−JDG−N−MA−H0JIGK−D−LB−I−J0−H−F+ME+LK−C+J−IH0]{\displaystyle A\lambda _{1}+...+N\lambda _{14}={\begin{bmatrix}0&C&-B&E&-D&-G&F-M\\-C&0&A&F&-G+N&D-K&-E-L\\B&-A&0&-N&M&L&-K\\-E&-F&N&0&-A+H&-B+I&C-J\\D&G-N&-M&A-H&0&J&I\\G&K-D&-L&B-I&-J&0&-H\\-F+M&E+L&K&-C+J&-I&H&0\\\end{bmatrix}}}It's exactly the Lie algebra of the group G2={g∈SO(7):g∗ϕ=ϕ,ϕ=ω123+ω145+ω167+ω246−ω257−ω347−ω356}{\displaystyle G_{2}=\{g\in SO(7):g^{*}\phi =\phi ,\phi =\omega ^{123}+\omega ^{145}+\omega ^{167}+\omega ^{246}-\omega ^{257}-\omega ^{347}-\omega ^{356}\}}

### Representations[edit]

The characters of finite-dimensional representations of the real and complex Lie algebras and Lie groups are all given by the Weyl character formula. The dimensions of the smallest irreducible representations are (sequence A104599 in the OEIS):

1, 7, 14, 27, 64, 77 (twice), 182, 189, 273, 286, 378, 448, 714, 729, 748, 896, 924, 1254, 1547, 1728, 1729, 2079 (twice), 2261, 2926, 3003, 3289, 3542, 4096, 4914, 4928 (twice), 5005, 5103, 6630, 7293, 7371, 7722, 8372, 9177, 9660, 10206, 10556, 11571, 11648, 12096, 13090….The 14-dimensional representation is the adjoint representation, and the 7-dimensional one is action of G2 on the imaginary octonions.

There are two non-isomorphic irreducible representations of dimensions 77, 2079, 4928, 28652, etc. The fundamental representations are those with dimensions 14 and 7 (corresponding to the two nodes in the Dynkin diagram in the order such that the triple arrow points from the first to the second).

Vogan (1994) described the (infinite-dimensional) unitary irreducible representations of the split real form of G2.

### Finite groups[edit]

The group G2(q) is the points of the algebraic group G2 over the finite field Fq. These finite groups were first introduced by Leonard Eugene Dickson in Dickson (1901) for odd q and Dickson (1905) for even q. The order of G2(q) is q6(q6 − 1)(q2 − 1). When q ≠ 2, the group is simple, and when q = 2, it has a simple subgroup of index 2 isomorphic to 2A2(32), and is the automorphism group of a maximal order of the octonions. The Janko group J1 was first constructed as a subgroup of G2(11). Ree (1960) introduced twisted Ree groups 2G2(q) of order q3(q3 + 1)(q − 1) for q = 32n+1, an odd power of 3.

### See also[edit]

### References[edit]

- ^ Agricola, Ilka (2008). "Old and new on the exceptional group G2" (PDF). Notices of the American Mathematical Society. 55 (8): 922–929. MR 2441524.
- ^ Élie Cartan (1893). "Sur la structure des groupes simples finis et continus". C. R. Acad. Sci. 116: 784–786.
- ^ Gil Bor and Richard Montgomery (2009). "G2 and the "rolling distribution"". L'Enseignement Mathématique. 55: 157–196. doi:10.4171/lem/55-1-8.
- ^ John Baez and John Huerta (2014). "G2 and the rolling ball". Trans. Amer. Math. Soc. 366: 5257–5293. arXiv:1205.2447 . doi:10.1090/s0002-9947-2014-05977-1.
- ^ Friedrich Engel (1900). "Ein neues, dem linearen Komplexe analoges Gebilde". Leipz. Ber. 52: 63–76,220–239.
- ^ Élie Cartan (1908). "Nombres complexes". Encyclopedie des Sciences Mathematiques. Paris: Gauthier-Villars. pp. 329–468.
- ^ Élie Cartan (1914), "Les groupes reels simples finis et continus", Ann. Sci. Ecole Norm. Sup., 31: 255–262

- Adams, J. Frank (1996), Lectures on exceptional Lie groups, Chicago Lectures in Mathematics, University of Chicago Press, ISBN 978-0-226-00526-3, MR 1428422
- Baez, John (2002), "The Octonions", Bull. Amer. Math. Soc., 39 (2): 145–205, doi:10.1090/S0273-0979-01-00934-X .

- Bryant, Robert (1987), "Metrics with Exceptional Holonomy", Annals of Mathematics, 2, 126 (3): 525–576, doi:10.2307/1971360
- Dickson, Leonard Eugene (1901), "Theory of Linear Groups in An Arbitrary Field", Transactions of the American Mathematical Society, Providence, R.I.: American Mathematical Society, 2 (4): 363–394, doi:10.1090/S0002-9947-1901-1500573-3, ISSN 0002-9947, JSTOR 1986251, Reprinted in volume II of his collected papers Leonard E. Dickson reported groups of type G2 in fields of odd characteristic.
- Dickson, L. E. (1905), "A new system of simple groups", Math. Ann., 60: 137–150, doi:10.1007/BF01447497 Leonard E. Dickson reported groups of type G2 in fields of even characteristic.
- Ree, Rimhak (1960), "A family of simple groups associated with the simple Lie algebra of type (G2)", Bulletin of the American Mathematical Society, 66 (6): 508–510, doi:10.1090/S0002-9904-1960-10523-X, ISSN 0002-9904, MR 0125155
- Vogan, David A. Jr. (1994), "The unitary dual of G2", Inventiones Mathematicae, 116 (1): 677–791, doi:10.1007/BF01231578, ISSN 0020-9910, MR 1253210

en.wikipedia.org

## Смотрите также

- The south the north
- Norton unerase
- Systemworks norton
- Norton security premium
- Norton free antivirus
- Norton security что это за программа
- Norton ghost portable
- Norton internet security 2017
- Norton 2017
- Dmz north korea
- Nords heroes of the north