An hydrogen atom moves with a velocity u and makes a head on inelastic collision with another stationary H-atom. Both atoms are in ground state before collision. The minimum value of u if one of them is to be given a minimum excitation energy is

Options

A. `2.64xx10^(4)ms^(-1)`
B. `6.24xx10^(4)ms^(-1)`
C. `2.02xx10^(6)ms^(-1)`
D. `6.24xx10^(8)ms^(-1)`

Answer

B

Explanation

As, mu=`2mv implies v=(u)/(2)`
`implies DeltaR=(1)/(2)m u^(2)-(1)/(2)(2m)((u)/(2))^(2)=(m u^(2))/(4)`
`implies (1)/(4) m u^(2)=13.6((1)/(1^(2))-(1)/(2^(2)))`
`implies (1)/(4)(1.0078)(1.66xx10^(-27))u^(2)=10.2xx1.6xx10^(-19)`
`implies u=6.24xx10^(4)ms^(-1)`