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Atoms
1
...
When an αparticle of mass m and velocity v moves
directly towards a nucleus of atomic number
Z, its distance of closest approach is given by
𝑟0 =
1

2𝑘𝑍𝑒 2 4𝑘𝑍𝑒 2
=
𝐸
𝑚𝑣 2

where 𝐸 = 2 𝑚𝑣 2
1

and 𝑘 = 4𝜋𝜀 = 9 × 109 𝑁𝑚2 𝐶 −2
...
Bohr's atom model
...
An atom consists of a
small massive central core called nucleus around
which planetary electrons revolve
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3
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An electron
having charge - e revolves with speed v in a
circular orbit of radius r round the nucleus
having charge + e
...

𝑛ℎ
𝑛
137
𝑛
2𝜋𝑘𝑒 2
where α =
is fine structure constant
...
36 𝑍2
= − 2 = − 2 𝑒𝑉
𝑛
𝑛

En = K
...
+ P
...
=
(ii) Quantum condition
...

2𝜋
where n is called principal quantum number
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While revolving in the
permissible orbits, an electron does not radiate
energy
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(iv) Frequency condition
...
If E1 and E2 are the energies
associated with these permitted orbits, then the
frequency v of the emitted or absorbed
radiation is given by
hv = E2 – E1

=−

𝑘𝑍𝑒 2
o
2𝑟

2𝜋2 𝑚𝑘 2 𝑒 4

where R = 𝑐ℎ3
= 1
...

4
...
Whenever
an electron makes a transition from a higher
energy level n2 to a lower energy level n1, the
difference of energy appears in the form of a
photon of frequency v given by
2𝜋 2 𝑚𝑘 2 𝑍 2 𝑒 4 1
1
[ 2 − 2]
3
ℎ
𝑛1 𝑛2
Wave number,
1 ∨ 2𝜋 2 𝑚𝑘 2 𝑍 2 𝑒 4 1
1
𝑣= = =
[ 2 − 2]
3
𝜆 𝑐
ch
𝑛1 𝑛2
𝑣=

1

1

]

or 𝑣 = 𝜆 = 𝑅𝑍 2 [𝑛2 − 𝑛2 ]
1

2

Different spectral series for hydrogen atom are
as follows:
(i) Lyman Series
...

This series lies in the ultraviolet region
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2

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...
com/@ArvindAcademy

1

(ii) Balmer Series
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and n
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𝑣=

1
1
1
= 𝑅 [ 2 − 2 ] , 𝑛2 = 3, 4,5, … …
𝜆
2
𝑛2

(iii) Paschen Series
...
and
n1 = 3
...

1

1

1

𝑣 = 𝜆 = 𝑅 [32 − 𝑛2 ] , 𝑛2 = 4, 5, 6,……
2

(iv) Brackett Series
...
This series lies in the infrared region
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𝜆
4
𝑛2
(v) Pfund Series
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and n1 = 5
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1
1
1
𝑣 = = 𝑅 [ 2 − 2 ] , 𝑛2 = 6, 7, 8, … …
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