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A H-atom moving with speed v makes a hea...

A H-atom moving with speed v makes a head on collision with a H-atom in rest. Both atoms are in ground state. Find the minimum value of velocity v for which one of atom may excite.

A

`6.25times10^(4)m//s`

B

`8times10^(4)m//s`

C

`7.25times10^(4)m//s`

D

`13.6times10^(4)m//s`

Text Solution

Verified by Experts

The correct Answer is:
A
For `v_(min)'`collision should be completely inelastic.According to energy conservation principle,
`1/2mv_(min)^(2)=1/2mv^(2)+1/2mv^(2)+DeltaE......(i)`
According to momentum conservation principle,
`mv_(min)=mv+mv`
`v=(v_(min))/2` …..(ii)
After solving Eqs.(i),we get
`(1/2)mv_(min)^(2)=2DeltaE`
`thereforev_(min)=sqrt(((4DeltaE)/m))`
Here, `DeltaE=`minimum excitation energy=`10.2 eV`
`m=1.67times10^(-27)kg`
`thereforev_(min)=sqrt(((4times10.2times1.6times10^(-19))/(1.67times10^(-27))))= 6.25times10^(4)m//s`
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