Find the wavelength of the radiation by hydrogen in the transition (a) `n = 3 to n = 2, n = 5 to n = 4 and n = 10 to n = 9`

Answer

A, B, C, D

Explanation

We know `bar lambda = 1//lambda`
`=1.1 xx 10^7((1)/(n_1^2)-(1)/(n_2^2))`
(a) `n_1 = 4` `n_2 = 3`
then `(1)/(lambda) = 1.1 xx 10^7 xx (1/4 - 1/9)`
` or ` lambda= (36)/(5 xx 11 xx 10^7)`
`=6.54 xx 10^-7= 654 nm`
`(b) `n_1 = 4` ,` n_2 = 5`
`bar lambda = 1.1 xx 10^-7((1)/(16)-(1)/(25))`
or `lambda = (400)/(1.1 xx 10^7 xx 9)`
`=40.404 xx 10^7m`
`=4040.4 nm`
for ` R= 1.097 xx 10^7 lambda`
`=4050 nm`
(c) `n_1 = 9`, `n_2 = 10`
`1/lambda = 1.1 xx 10^7((1)/(81)-(1)/(100))`
`lambda = (81 xx 100)/(19 xx 11 xx 10^7)`
`=387.5598 xx 10^-7 m`
`=3875509 nm`
`R=1.097 xx 10^7 lambda`
`=38861.9`