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Q.

A hydrogen atom (at ground state) of kinetic energy k, head on collides with stationary helium atom (at ground state). Find minimum value of k for which after collision, photons corresponding to Balmer series of hydrogen and Lyman series of helium are emitted :

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a

80 eV

b

51 eV

c

66.2 eV

d

15.1 eV

answer is A.

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Detailed Solution

Maximum possible loss
$= \frac{1}{2} (\frac{m \times 4 m}{m + 4 m}) v^{2} = \frac{4 k}{5}$
$= 12.1 + 40.8 = 52.9$
$\Rightarrow \frac{4 k}{5} = 52.9 \Rightarrow k = 66.2 e V$

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