v20

Options

A. `lamda=sqrt(lamda_1lamda_2)`
B. `lamda=(lamda_1lamda_2)/2`
C. `2/lamda=1/lamda_1+1/lamda_2`
D. `1/lamda_2=1/lamda_1^2+1/lamda_2^2`

Answer

D

Explanation

Linear momentum of particles before collision is given as follows
`p_1=h/lamda_1 And , p_2=h/lamda_2`
Particles are moving along perpendicular directions, hence for inelastic collision net linear momentum of the final particle can be written as follows .
`p=sqrt(p_1^2+p_2^2)`
`impliesh/lamda=sqrt((h/lamda_1)^2+(h/lamda_2)^2)`
`implies1/lamda_2=1/lamda_1^2+1/lamda_2^2`