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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 excited state. Subsequently `H` atoms transfer their total excitation energy to `He+` ions (by collisions) Assume that the bohr model of atom is exactly valid.
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

`5.6 xx 10^(-7) m`

C

`4.8 xx 10^(-7) m`

D

`4.0 xx 10^(-7) m`

Text Solution

Verified by Experts

Visible light lies in the range, `lambda_(1) = 4000 Å to lambda_(2) = 7000 Å`. Energy of photons corresponding to these wavelength (in eV) would be :
`E_(1) = (12375)/(4000) = 3.09 eV`, and
`E_(2) = (900)/(11 R) = 1.77eV`
From energy level diagram of `He^(+)` atom, we can see that in transition from `n = 4 to n = 3`, energy of photon released will lie between `E_(1)` and `E_(2)`.
`Delta E_(43) = - 3.4 (- 6.04)`
`= 2.64 eV`
wavelength to photon corresponding to this energy.
`lambda = (12375)/(264) Å = 4687.5 Å`
`= 4.68 xx 10^(-7) m`
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