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At what minimum kinetic energy must a hy...

At what minimum kinetic energy must a hydrogen atom move for it's inelastic headon collision with another stationary hydrogen atom so that one of them emits a photon? Both atoms are supposed to be in the ground state prior to the collision.

A

20.4 eV

B

36.3 eV

C

108.8 eV

D

122.4 eV

Text Solution

Verified by Experts

The correct Answer is:
A
The loss in kinetic energy should be 10.2 eV so that, the case of the hydrogen atom may be excited to first excited state. For minimum kinetic enegy, the two atoms will move together.
`mv_(0)=(m+m)v rArr v=v_(0)/2`
Loss in kinetic energy `=1/2mv_(0)^(2)-1/2(2m)(v_(0)/2)^(2)`
`10.2 eV=1/4mv_(0)^(2)=1/2(K)`
`therefore K=2 times 10.2 eV=20.4 eV`
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