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If lambda(1) and lambda(2) are the wavel...

If `lambda_(1)` and `lambda_(2)` are the wavelengths of the first members of the Lyman and Paschen series respectively, then `lambda_(1) : lambda_(2)` is

A

`1:3`

B

`1:30`

C

`7:50`

D

`7:108`

Text Solution

Verified by Experts

The correct Answer is:
D
For Lyman series , `n_(1)=1` and `n_(2)=2` for first line.
`therefore (1)/(lambda_(1))=R[(1)/(1^(2))-(1)/(2^(2))]=R[(1)/(1)-(1)/(4)]=(3R)/(4)`
For Paschen series, `n_(1)=3` and `n_(2)=4` for `1^(st)` line.
`therefore (1)/(lambda_(2))=R[(1)/(3^(2))-(1)/(4^(2))]=R[(1)/(9)-(1)/(16)]=(7R)/(144)`
`(lambda_(1))/(lambda_(2))=(4//3R)/(144//7R)=(4)/(3R)xx(7R)/(144)=(7)/(108)`.
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