02 Atomic Structure Formula Sheets
02 Atomic Structure Formula Sheets
02 Atomic Structure Formula Sheets
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ATOMIC STRUCTURE
2 2 Z 2 e4 m Z2
En erg / electron 2.178 1018 J 2
h2n2 n
[1]
[2] ATOMIC STRUCTURE
Wheren, Z-atomic number; m and e are mass and charge of the electron respectively.
The radius of the paths in which can electron can revolve is given by
n 2h 2
r 0.53n 2 Å
42 me 2 Z
(1 Å = 10–8 cm)
When an electron jumps from an outer orbit in which its quantum number is ‘n2’ to an inner orbit in which it is ‘n1’;
the energy emitted as radiation is given by :
2 2 Z2 e 4 m 1 1
E n 2 E n1
h2 n 21 n 2
2
2 2 Z2 e 4 m 1 1 1 1
3 2 2 R 2 2
hc n1 n 2 n1 n 2
where R is the Rydberg constant. For hydrogen, R is 109677.8 cm–1.
We can concluded two important points from Bohr model :
(a) The model correctly fits the quantized energy level of the hydroen atom as infered from, its emission
spectrum. These energy level correspond o certain allowed circular orbitas for the electrons.
(b) As the electron becomes more tightly bound, its energy becomes more negative relative to the zero energy
reference state (corresponding to the electron being an infinite distance fom the nucleus) ie as the electron
is brought closer to the nucleus, enegy is released from the system.
(c) A general equation for the electron moving from one level (ninitial) to another level (nfinal):
E = energy of level nfinal – energy of level ninitial = Efinal – Einitial
12 2
(2.178 1018 J) 2 (2.178 1018 J) 2
n final n initial
12 12
2.178 1018 J 2 2
n final n initial
8. Modern structure of Atom : Atom consists of two parts (A) Nucleus (B) Extra nuclear particles called
electrons.
(A) Nucleus : The nucleus of an atom has a radius of about 10-13 cm whereas the atomic radius is about
1 × 1–8 cm. The nucleus contains different kinds of particles known as nuclear particles or nucleon. The
various nuclear particles are as follows :
(a) Proton (H+ or p) : The characteristics of a proton are as follows :
(i) Absolute mass = 1.66 × 10–24 g
(ii) Relative mass = 1 amu
(iii) Relative charge = + 1 unit
(iv) Absolute charge = + 1.6 × 10–19 coulomb = + 4.8 × 10–10 e.s.u.
(v) Atomic number = + 1
(vi) Inventor : Goldstein in 1886 in “anode Rays Experiments”.
(b) Positron (e+) :
(i) It is an antiparticle of electron because it has same negligible mass and same amount of charge as
of the electron but he charge is +ve.
ATOMIC STRUCTURE [3]
shell in which particular electron is present. It mainly decides the energy of the electron in the orbit. It also
gives the no. of electrons that may be accomodated in each shell. The capacity of each shell being given as
2n2. It decides the size of the shell.
nh
mvr
2
22 mZ2 e 4
E
h2
E = Energy of electron in a particular level,
e = Electron charge, m = Mass of electron,
Z = Atomic number, h = Planck’s constant.
(b) Azimuthal or secondary or subsidiary quantum number ‘l’ : It represents the no. of subshells can have
the values 0 to (n – 1). It gives the shape of he subshell.
The volume of space where probability of finding an electron is maximum, is called orbital or subshell.
Properties : s p d f g
shape Spin Dumb-bell Double Complicated –
dumb-bell
No. of sub-
subshells 1 3 5 7 9
l 0 1 2 3 4
Max. no. of 2 6 10 14 18
electrons
h
mvr l(l 1)
2
z z z z z
y y y y y
x x x x x
(c) Magnetic quantum no. ‘m’ : This gives he no. of orbitals in a subshell (under the influence of magnetic
field). It takes only integral values rom – l to + l through zero m = 2l +1 for any value of l,
m = n2
e l= 0m= 1
In s-subshell there is only one sub-subshell.
In p-subshell there are px py pz where x, y, z refer to the axis perpendicular to each other.
In d-subshell there are dxy, dyz, dzx, d x2 y2 and d z 2
In f-subshell there are 7 orbitals.
(d) Spin quantum no. ‘s’ : When an electron rotates around a nucleus, it spins around its axis. It spin os
1 1
cockwise it is written as as or . If anticlockwise then it is or (even no. e).
2 2
ATOMIC STRUCTURE [5]
h s(s 1)
mvr
2
We can write allowed combinations of quantum numbers for the first four shells as below :
n l m Orbital Number of Number of
rotation orbitals in orbitals in
subshell shell
1. 0 0 1s 1 1
0 0 2s 1 4
2.
1 -1, +1 2p 3
0 0 3s 1 9
3. 1 -1,0, +1 3p 3
2 -2, -1,0,+1,+2 3d 5
0 0 4s 1 16
1 -1,0, +1 4p 3
4
2 -2, -1, 0, +1, +2 4d 5
3 -3, -2, -1, 0, +1, +2, +3 4f 7
7s 7p 7d 7f
6s 6p 6d 6f
5s 5p 5d 5f
4s 4p 4d 4f
3s 3p 3d
2s 2p
1s
C:
1s 2s 2p
N:
1s 2s 2p
O:
1s 2s 2p
1
11th electron ; n = 3, l = 0, m = 0, s = +
2
1
12th electron ; n = 3, l = 0, m = 0, s = –
2
ATOMIC SPECTRA
When the sunlight is passed through prism, it is dispersed into 7 colour which is called as spectra. If the atom is
excited and then examined through spectroscope. We see no. of lines. This is called line spectra or atomic
spectra.
1. Atomic spectra of hydrogen
Bohr (1913) proposed that an electron moves only in the orbit in which angular momentum of the electron is equal
2h
to . Such orbits are called ‘Stationary States’ by Bohr..
2
When an electron jumps from one orbit to anoher it either loses or gains energy in he form of radiation. The
energy of radiation is given by :
E2 – E1 = hv
E 2 E1
or
h
c E 2 E1
or
h
1 E 2 E1
or
ch
Therefoe line in the spectrum of ‘H’ results from the dropping of electron excited to hiher stationary states back
to lower, or less energetic states. Each line was ascribed to a transfer to the electron from an orbit of some n
[8] ATOMIC STRUCTURE
value to an orbit of some lower n value. Using this, Bohr was able to account for the observed wavelength of the
lines in Lyman, Balmer and Paschen series.
l 1 1
RH 2 2
n1 n 2
where RH = Rydberg’s constanat
n1 = 1 for Lyman
= 2 for Blamer
= 3 for Paschen
= 4 for Brackett
= 5 for Pfund
It failed to systems conaining more than on electron.
2. The hydrogen atom
It can be discussed as below :
(a) In quantum mechanical model the electron is described as a wave. Thsi representation leads to a series of
wave functions (orbitals) that describe the possible energies and special distributions available to the electorn.
(b) In agreement with the Heisenberg’s uncertainty principle, the model cannot specify the detailed electron
motons. nstead, the square of the wave function represents the probability distribution of the electron in that
orbital. This approach allows us to picture orbitals in terms of probability distributions, or electron density
maps.
(c) The size of an orbital is arbitarily defnied as the surface that contains 90% of the total electron probability.
(d) The hydrogen atom has many types of orbitals. n the ground state the single electron resides in the 1st
orbital. The electron can be excited to higher energy orbitals if the atom absorbs energy.
3. Few Terms
(a) Mass Defect : Actual mass of atom is not equal to the sum of mass of e, p and n present in it, eg for chlornie
35
17Cl = 17 (1.007276) amu + 18(1.008665) amu + 17.(0.0005486) amu = 35.289005 amu
However, the mass of chlorine has been accurately determined as 34.96885 amu. This difference between
the two values (35.28901 amu – 34.96885 amu) = 0.32016 amu is known as mass defect.
This difference, expressed in its energy equivalent, is called the binding energy of the nucleons (neutrons +
protons) in the nucleus of the atom in questions.
(b) Isotopes : Atoms of an element havnig the same atomic no., but different at. wt. are called isotopes.
35 37
e.g. Cl and 17
17 Cl; 11H, 12 D and 13T; 16 17 18
8 O, 8 O and 8 O
Isotopes have the same no. of protons and electrons but different no. of neutrons. They have the same
chemical properties. The fractional at. wt. of an element is due to the different proportion in which vaious
ATOMIC STRUCTURE [9]
isotopes are present in it, eg chlorine has two isotopes 17Cl35 and 17Cl37 present in the ratio 3 : 1.
3 35 1 37
Average at. wt. 35.5 amu
4
(c) Iobars : Atoms having the same no. of neutrons but different no. of protons are called isotones, eg.
30 31
14 Si, 15 P
(e) Isoelectronic ions or Molecules : Species having same no. of electron but different charge of nucleus
are known as Isoelectronic ions, e.g.
(i) O2–, F-, Ne, Na+, Mg2+, Al3+
(ii) NO3–, CO32–, COCl2
(iii) NH3, H3O+
(iv) N2, CO, CN–
(v) NCs– and Cs2
(vi) H–, He, Li+
(f) Isodiaphers : Atoms having same isotopic numbers. i.e. same value of (n–p) but different atomic as well
as mass number.