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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Atoms Molecules and Nuclei Page 3

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5.

Origin of Spectral Lines

 

 

(i)

Wave number

1

 

l

(1)

Start with third postulate

 

hu = En2 - En1

...(1)

(2)

Substitute n = n2 and n = n1 in the equation En = -

m e4

1

 

 

8e02h2

n2

 

En2 - En1 =

m e4

1

-

1

 

...(2)

 

 

 

8e02 h2

n12

n22

(3)

Using 

1

=

u

 

 

l

c

 

From (1) and (2),

 

 

1

=

m e4

1

-

1

 

 

 

 

l

8e02h3c

n12

n22

 

where R =

m e4

is called Rydberg's constant.

 

8e02ch3

 

\

1

=

R

1

-

1

 

 

 

l

n12

n22

 

\ Wave number

1

=

R

1

-

1

 

 

 

l

n12

n22

(ii) Hydrogen Spectrum:

 

Name of series

n1

Formula

Region

Lyman

1

\

1

=

R

1

-

1

n2 = 2, 3, 4,.

 

 

 

l

12

n22

Ultraviolet

Balmer

2

\

1

=

R

1

-

1

n2 = 3, 4, 5,

 

 

 

l

22

n22

Visible

Paschen

3

\

1

=

R

1

-

1

n2 = 4, 5, 6,

 

 

 

l

32

n22

Infrared

Brackett

4

\

1

=

R

1

-

1

n2 = 5, 6, 7,

 

 

 

l

42

n22

Infrared

Pfund

5

\

1

=

R

1

-

1

n2 = 6, 7, 8,

 

 

 

l

52

n22

Infrared

 

 



 

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