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Question

If λ1 and λ2 are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of λ1:λ2 is:

A
1:3
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B
1:9
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C
7:135
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D
7:108
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Solution

The correct option is C 7:135
For Lyman series :

n1=1,n2=4

1λ1=RZ2(112142)

1λ1=RZ2(1611×16)

1λ1=RZ2(151×16)

λ1=1615RZ2

For paschen series :

n1=3,n2=4

1λ2=RZ2(132142)

1λ2=RZ2(1699×16)

1λ2=RZ2(79×16)

λ2=9×167RZ2

So ,

λ1λ2=1615RZ29×167RZ2

λ1λ2=16×715×9×16

λ1λ2=7135

λ1λ2=7:135

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