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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

The correct Answer is:
C
The wavelength corresponding to transition from `n = 4` to `n=3` in `He+` corresponds to visible region. Its wavelength is :
`(hc)/(lamda)=13.6 xx 4[(1)/(9)-(1)/(16)]`
`(4.1 xx 10^(-15)xx3 xx10^(8))/(lamda(m)) =13.6 xx 4 xx (7)/(9 xx 16)`
`rArr lamda=(4.1 xx 10^(-15)xx3 xx10^(8))/(13.6 xx4 xx(7)/(9 xx 16))m`
`lamda = 4.68 xx 10_(-7) m`
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