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Question

A stationary hydrogen atom of mass m in the ground state achieves minimum excitation energy after head-on, inelastic collision with a moving hydrogen atom. Find the velocity of moving hydrogen atom:


A

[10.2(eV)m]12

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B

[40.8(eV)m]12

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C

[20.4(eV)m]12

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D

[40.8(eV)1.0078 m]12

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Solution

The correct option is B

[40.8(eV)m]12


Applying conservation of linear momentum,

mu=2mv;v=u2

ΔE=12mu212×2m×v2=14mu2

Minimum excitation energy is to excite a hydrogen atom from ground state to first excited state.

=3.4(13.6)eV=10.2eV

14mu2=10.2eV

u=[40.8(eV)m]12


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