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The shortest wavelength of the line in h...

The shortest wavelength of the line in hydrogen atomic spectrum of Lyman series when `R_(H) = 109678 cm^(-1)` is

A

a)`1002.7Å`

B

b)`1215.67 Å`

C

c)`1127.30 Å`

D

d)`911.7Å`

Text Solution

Verified by Experts

The correct Answer is:
D
Rydberg.s formula is
`(1)/(lamda ) = R_(H) Z ^(2) ((1)/( n _(1) ^(2)) - (1)/( n _(2) ^(2)))`
For hydrogen,
z =1 and for lyman series, `n _(1) =1 and n _(2) = oo`
(for shortest wavelength)
On substituting values, we get
`(1)/(lamda ) = 1096 78 xx(1)^(2) xx [ (1)/((1) ^(2) ) - (1)/((oo) ^(2))]`
`(1)/(lamda) = 109678 cm ^(-1)`
or `lamda = (1)/( 109678) cm ^(-1)`
`= 9.117 xx 10 ^(-6) cm`
`= 91.1 7 xx 10 ^(-8) cm`
`= 911.7 Å`
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