First slide

Wave nature of matter

Question

A photon of wavelength 0.1 $\overset{o}{A}$ is emitted by a helium atom as a consequence of the emission of photon. The KE gained by helium atom is

Moderate

A

0.05 eV
B

1.05 eV
C

2.05 eV
D

3.05 eV

Solution

$\begin{matrix} E = \frac{p^{2}}{2 m} = \frac{h^{2}}{2 m λ^{2}} \\ = \frac{{(6.62 \times 10^{- 34})}^{2}}{2 \times 4 \times 1.67 \times 10^{- 27} \times {(0.1 \times 10^{- 10})}^{2}} \times \frac{1}{1.6 \times 10^{- 19}} eV \\ = \frac{43.82 \times 10^{- 68}}{21.376 \times 10^{- 68}} = 2.05 eV \end{matrix}$

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