Both nucleus and atom of some element are in their respective first excited states. They get de-exci

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11.Dual Nature of Radiation and matter

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Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths $\lambda _N,\,\lambda _A$ respectively. The ratio $\frac{{{\lambda _N}}}{{{\lambda _A}}}$ is closest to

A

$10^{-6}$

B

$10$

C

$10^{-1}$

D

$10^{-10}$

(JEE MAIN-2018)

Solution

Energy $E = \frac {hc}{\lambda };$

$\frac{{{\lambda _N}}}{{{\lambda _A}}} = \frac{{{E_A}}}{{{E_N}}}$

where $E_A$ and $E_N$ are energies of photons from atom and nucleus respectively. $E_N$ is of the order of $MeV = 10^6\,\,eV$ and $E_A$ in few $eV.$

So $\frac{{{\lambda _N}}}{{{\lambda _A}}}\, = \,{10^{ – 6}}$

Standard 12

Physics

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