# The wavelengths involved in the spectrum of deuterium $\dpi{100} \left ( _{1}^{2} D\right )$ are slightly different from that of hydrogen spectrum, because Option 1) size of the two nuclei are different Option 2) nuclear forces are different in the two cases Option 3) masses of the two nuclei are different Option 4) attraction between the electron and the nucleus is different in the two cases.

As we learnt in

Effect of nucleas motion on radius of atom -

$r_{n}^{1}= r_{n}\left ( 1+\frac{m_{e}}{m_{N}} \right )$

- wherein

$r_{n}^{1}=$  Radius  of nth orbital with nucleus motion

$r_{n}=$ Radius of nth orbital without nucleus motion

$m_{e}=$mass of electron

$m_{N}=$mass of nucleus

Masses of    ${_{1}}H^{1}$    and   ${_{1}}D^{2}$ are different. Hence the corresponding wavelengths are different.

Correct option is 3.

Option 1)

size of the two nuclei are different

This is an incorrect option.

Option 2)

nuclear forces are different in the two cases

This is an incorrect option.

Option 3)

masses of the two nuclei are different

This is the correct option.

Option 4)

attraction between the electron and the nucleus is different in the two cases.

This is an incorrect option.

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