Shell Model of Nucleus

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Shell Model of Nucleus

Chemistry , Inorganic Chemistry

Shell Model of Nucleus

Shell Model of Atom

The proton configuration of an atom describes the orbitals occupied by protons on the nucleus. The basis of this prediction is the aufbau principle, which assumes that protons are added to an nucleus, one at a time, starting with the lowest energy orbital, until all of the protons have been placed in an appropriate orbital.
An easy way to calculate the total number of protons that can be held by a given energy level is to use the triangular numbers formula (n+1)*n , where n equals the number of the protons shell. For example, for the 1st proton shell n=1 and 2*1 = 2, telling us that the capacity of the 1st shell is 2 protons. For the 2nd shell ( n=2 ) and 3*2 = 6. For an atom to fill its 2nd proton shell, 8 protons would be needed : 2 to fill the 1st shell and 6 to fill the 2nd.

Principle energy level ( n )	Maximum number of protons *(n+1)n**
1	2
2	6
3	12
4	20
5	30
6	42
7	56

The number of sublevels that an energy level can contain is equal to the principle quantum number of that level. The first sublevel is called s sublevel. s sublevels have one orbital, which can hold up to two protons. The second sublevel is called a p sublevel. p sublevels have two orbitals, each of which can hold 2 protons, for a total of 4. The third sublevel is called a d sublevel and d sublevels have 3 orbitals, for a possible total of 6 protons. The fourth sublevel is called an f sublevel. f sublevels, with 4 orbitals, can hold up to 8 protons. The 6-th sublevel is called an h sublevel. h sublevels, with 6 orbitals, can hold up to 12 protons. The 7-th sublevel with 7 orbitals, can hold up to 14 protons. Although energy levels that are lower than 7 would contain additional sublevels, these sublevels have not been named because no known atom in its ground state would have protons that occupy them.

Orbital and Proton Capacity for the Sublevels
Sublevel	# of orbitals	Maximum number of protons
s	1	2
p	2	4
d	3	6
f	4	8
g	5	10
h	6	12
...	7	14
...	8	16

An easy way to calculate the total number of protons that can be held by a given energy sublevel is to use the formula for natural numbers: 2*k. where k=1,2,3,4,5,6, ....

Tables of sublevels in atom

sublevel	# of protons		# of neutrons		suma	# of electrons		suma
s	1	1			2	1	1	2
p	2	2	1	1	6	3	3	6
d	3	3	2	2	10	5	5	10
f	4	4	3	3	14	7	7	14
g	5	5	4	4	18	9	9	18
h	6	6	5	5	22	11	11	22

In the atomic shell model, the shells are filled with protons in order of increasing natural numbers series, producing the magic numbers. These elements have highly stable properties:

#	Case	Proton Configuration	Geometrical Number of protons	Real Number of protons
1	Geometrical	2	2
	He	2		2
2	Geometrical	2,2-4	8
	C	2,*-4		6
3	Geometrical	2,2-4,2-4-6	20
	Si	2,2-4,--6		14
4	Geometrical	2,2-4,2-4-6,2-4-6-8	40
	Ni	2,2-4,2-4-6,--*-8		28
5	Geometrical	2,2-4,2-4-6,2-4-6-8,2-4-6-8-10	70
	Sn	2,2-4,2-4-6,2-4-6-8,----10		50
6	Geometrical	2,2-4,2-4-6,2-4-6-8,2-4-6-8-10,2-4-6-8-10-12	112
	Pb	2,2-4,2-4-6,2-4-6-8,2-4-6-8-10,----*-12		82

The ground electronic and proton configurations of the elements H through U are given below.

				*Configuration*
Z		Symbol		Electron Configuration	Proton Configuration

1		H		1s¹	1s¹
2		He		1s²	1s²
3		Li		[He] 2s¹	[He] 2p¹
4		Be		[He] 2s²	[He] 2p²
5		B		[He] 2s² 2p¹	[He] 2p³
6		C		[He] 2s² 2p²	[He] 2p⁴
7		N		[He] 2s² 2p³	[He] 2p⁴ 2s¹
8		O		[He] 2s² 2p⁴	[He] 2p⁴ 2s²
9		F		[He] 2s² 2p⁵	[O] 3d¹
10		Ne		[He] 2s² 2p⁶	[O] 3d²
11		Na		[Ne] 3s¹	[O] 3d³
12		Mg		[Ne] 3s²	[O] 3d⁴
13		Al		[Ne] 3s² 3p¹	[O] 3d⁵
14		Si		[Ne] 3s² 3p²	[O] 3d⁶
15		P		[Ne] 3s² 3p³	[O] 3d⁶ 3p¹
16		S		[Ne]3s² 3p⁴	[O] 3d⁶ 3p²
17		Cl		[Ne] 3s² 3p⁵	[O] 3d⁶ 3p³
18		Ar		[Ne] 3s² 3p⁶	[O] 3d⁶ 3p⁴
19		K		[Ar] 4s¹	[O] 3d⁶ 3p⁴ 3s¹
20		Ca		[Ar] 4s²	[O] 3d⁶ 3p⁴ 3s²
21		Sc		[Ar] 3d² 4s²	[Ca] 4f¹
22		Ti		[Ar] 3d² 4s²	[Ca] 4f²
23		V		[Ar] 3d³ 4s²	[Ca] 4f³
24		Cr		[Ar] 3d⁵ 4s¹	[Ca] 4f⁴
25		Mn		[Ar] 3d⁵ 4s²	[Ca] 4f⁵
26		Fe		[Ar] 3d⁶ 4s²	[Ca] 4f⁶
27		Co		[Ar] 3d⁷ 4s	[Ca] 4f⁷
28		Ni		[Ar] 3d⁸ 4s²	[Ca] 4f⁸
29		Cu		[Ar] 3d¹⁰ 4s¹	[Ca] 4f⁸ 4d¹
30		Zn		[Ar] 3d¹⁰ 4s²	[Ca] 4f⁸ 4d²
31		Ga		[Ar] 3d¹⁰ 4s² 4p¹	[Ca] 4f⁸ 4d³
32		Ge		[Ar] 3d¹⁰ 4s² 4p²	[Ca] 4f⁸ 4d⁴
33		As		[Ar] 3d¹⁰ 4s² 4p³	[Ca] 4f⁸ 4d⁵
34		Se		[Ar] 3d¹⁰ 4s² 4p⁴	[Ca] 4f⁸ 4d⁶
35		Br		[Ar] 3d¹⁰ 4s² 4p⁵	[Ca] 4f⁸ 4d⁶ 4p¹
36		Kr		[Ar] 3d¹⁰ 4s² 4p⁶	[Ca] 4f⁸ 4d⁶ 4p²
37		Rb		[Kr] 5s¹	[Ca] 4f⁸ 4d⁶ 4p³
38		Sr		[Kr] 5s²	[Ca] 4f⁸ 4d⁶ 4p⁴
39		Y		[Kr] 4d¹ 5s²	[Ca] 4f⁸ 4d⁶ 4p⁴ 4s¹
40		Zr		[Kr] 4d² 5s²	[Ca] 4f⁸ 4d⁶ 4p⁴ 4s²
41		Nb		[Kr] 4d⁴ 5s¹	[Zr] 5g¹
42		Mo		[Kr] 4d⁵ 5s¹	[Zr] 5g²
43		Tc		[Kr] 4d⁵ 5s²	[Zr] 5g³
44		Ru		[Kr] 4d⁷ 5s¹	[Zr] 5g⁴
45		Rh		[Kr] 4d⁸ 5s¹	[Zr] 5g⁵
46		Pd		[Kr] 4d¹⁰	[Zr] 5g⁶
47		Ag		[Kr] 4d¹⁰ 5s¹	[Zr] 5g⁷
48		Cd		[Kr] 4d¹⁰ 5s²	[Zr] 5g⁸
49		In		[Kr] 4d¹⁰ 5s² 5p¹	[Zr] 5g⁹
50		Sn		[Kr] 4d¹⁰ 5s² 5p²	[Zr] 5g¹⁰
51		Sb		[Kr] 4d¹⁰ 5s² 5p³	[Zr] 5g ¹⁰ 5f¹
52		Te		[Kr] 4d¹⁰ 5s² 5p⁴	[Zr] 5g ¹⁰ 5f²
53		I		[Kr] 4d¹⁰ 5s² 5p⁵	[Zr] 5g ¹⁰ 5f³
54		Xe		[Kr] 4d¹⁰ 5s² 5p⁶	[Zr] 5g¹⁰ 5f⁴
55		Cs		[Xe] 6s¹	[Zr] 5g¹⁰ 5f⁵
56		Ba		[Xe] 6s²	[Zr] 5g¹⁰ 5f⁶
57		La		[Xe] 5d¹ 6s²	[Zr] 5g¹⁰ 5f⁷
58		Ce		[Xe] 4f¹ 5d¹ 6s²	[Zr] 5g ¹⁰ 5f⁸
59		Pr		[Xe] 4f³ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d¹
60		Nd		[Xe] 4f⁴ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d²
61		Pm		[Xe] 4f⁵ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d³
62		Sm		[Xe] 4f⁶ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d⁴
63		Eu		[Xe] 4f⁷ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d⁵
64		Gd		[Xe] 4f⁷ 5d¹ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d⁶
65	Tb	[Xe] 4f⁹ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d⁶ 5p¹
66	Dy	[Xe] 4f¹⁰ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d⁶ 5p²
67	Ho	[Xe] 4f¹¹ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d⁶ 5p³
68	Er	[Xe] 4f¹² 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d⁶ 5p⁴
69	Tm	[Xe] 4f¹³ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d⁶ 5p⁴ 5s¹
70	Yb	[Xe] 4f¹⁴ 6s²	[Zr] 5g ¹⁰ 5f⁸ 5d⁶ 5p⁴ 5s²
71	Lu	[Xe] 4f¹⁴ 5d¹ 6s²	[Yb] 6h¹
72	Hf	[Xe] 4f¹⁴ 5d² 6s²	[Yb] 6h²
73	Ta	[Xe] 4f¹⁴ 5d³ 6s²	[Yb] 6h³
74	W	[Xe] 4f¹⁴ 5d⁴ 6s²	[Yb] 6h⁴
75	Re	[Xe] 4f¹⁴ 5d⁵ 6s²	[Yb] 6h⁵
76	Os	[Xe] 4f¹⁴ 5d⁶ 6s²	[Yb] 6h⁶
77	Ir	[Xe] 4f¹⁴ 5d⁷ 6s²	[Yb] 6h⁷
78	Pt	[Xe] 4f¹⁴ 5d⁹ 6s¹	[Yb] 6h⁸
79	Au	[Xe] 4f¹⁴ 5d¹⁰ 6s¹	[Yb] 6h⁹
80	Hg	[Xe] 4f¹⁴ 5d¹⁰ 6s²	[Yb] 6h¹⁰
81	Tl	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p¹	[Yb] 6h¹¹
82	Pb	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p²	[Yb] 6h¹²
83	Bi	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p³	[Yb] 6h¹² 6g¹
84	Po	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p⁴	[Yb] 6h¹² 6g²
85	At	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p⁵	[Yb] 6h¹² 6g³
86	Rn	[Xe] 4f¹⁴ 5d¹⁰ 6s² 6p⁶	[Yb] 6h¹² 6g⁴
87	Fr	[Rn] 7s¹	[Yb] 6h¹² 6g⁵
88	Ra	[Rn] 7s²	[Yb] 6h¹² 6g⁶
89	Ac	[Rn] 6d¹ 7s²	[Yb] 6h¹² 6g⁷
90	Th	[Rn] 6d² 7s²	[Yb] 6h¹² 6g⁸
91	Pa	[Rn] 5f² 6d¹ 7s²	[Yb] 6h¹² 6g⁹
92	U	[Rn] 5f³ 6d¹ 7s²	[Yb] 6h¹² 6g¹⁰

Today, our knowledge about nuclei, is restricted to about 2500 of the potentially existing 6000 combinations of protons and neutrons (see Figure ).

Black squares indicate the stable nuclei.

*****************************************

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tejas

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19 Mar 2009 17:35:59 IST

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a bit too long....but usefull..!!!

akhil

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19 Mar 2009 18:13:21 IST

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nice1

saharsha kumar keshkar

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22 Mar 2009 17:46:30 IST

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thanks!

debotosh the competitor

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22 Mar 2009 18:31:19 IST

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copied n bogus n uninteresti ng

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Shell Model of Atom

Principle energy
level ( n )

Maximum number
of protons **(n+1)*n**

1

2

2

6

3

12

4

20

5

30

6

42

7

56

Comments (4)

Quick Reply

Reply

Preparing for IIT-JEE ?

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Shell Model of Atom

Principle energy level ( n )

Maximum number of protons (n+1)*n

1

2

2

6

3

12

4

20

5

30

6

42

7

56

Comments (4)

Quick Reply

Reply

Preparing for IIT-JEE ?

Arihant Revision Package for IIT JEE - Books, Practice Tests + Rank Predictor

@ INR 1,995/-

For Quick Info

Principle energy
level ( n )

Maximum number
of protons **(n+1)*n**