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In a mixture of H- He^(+) gas (He+ is si...

In a mixture of `H- He^(+)` gas (`He+ `is singly ionized He atom), `H` atom and `He+` ions are excited to their respective first sxcited state subequendy `H` atoms transfer their total excilation energy to `He+` ions (by collsions) Assume that the bohr model of atom is exactly veld.
The wavelength of light emitted in the visible region by `He+` lons after collisions with `H` atoms is -

A

`6.5 xx 10^(-7) m `

B

`3.6 xx 10^(-7) m `

C

`4.8 xx 10^(-7) m `

D

`4.0 xx 10^(-7) m `

Text Solution

Verified by Experts

The correct Answer is:
C
After collsionwith hydrogen atom rthe `He^(+)` ion is in its third excitwed state `(n = 4 )` After that the electron can jump into `n = 3`
`deltaE = hv = (hc)/(lambda) = E_(4) - E_(3)`
`= [(-13.6 xx 4)/(16) - ((-13.6 xx 4 )/(9))] xx 1.6 xx 10^(-19)`
`:. (6.6 xx 10^(-34) xx 3 xx 10^(8))/(lambda) = - 13.6 xx 4 [(1)/(16) - (1)/(9)]`
:. lambda = (6.6 xx 10^(-34) xx 3 xx 10^(8) xx 9 xx 16 )/(7 xx 13.6 xx 4 xx 1.6 xx 10^(-19)) = 4.68 xx 10^(-7) m `
Since only one option is currect , we need not work out the case of electron jumping from `n = 4 to n = 2 `
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