A neutron travelling with a velocity `v` and kinetic energy `E` collides perfectly elastically head on with the nucleus of an atom of mass number `A` at rest. The fraction of the total kinetic energy retained by the neutron is

Options

A. `((A-1)/(A+1))^(2) `
B. ` ((A+1)/(A-1))^(2) `
C. ` ((A-1)/(A))^(2) `
D. ` ((A+1)/(A))^(2) `

Answer

A

Explanation

` ((Delta K)/( K)) _(" retained") =((m_1-m_2)/(m_1+m_2) ) ^(2) = ((1-A)/(1+A))^(2) `