A neutron travelling with a velocity v and kinetic energy E has a perfectly elastic head-on collision with a nucleus of an atom of mass number A at rest. The fraction of total energy retained by the neutron is approximately

$[\frac{A - 1}{A + 1}]^{2}$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$[\frac{A + 1}{A - 1}]^{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$[\frac{A - 1}{A}]^{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$[\frac{A + 1}{A}]^{2}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
$[\frac{A - 1}{A + 1}]^{2}$

$v_{1}^{'} = \frac{(m_{1} - m_{2}) v_{1} + 2 m_{2} v_{2}}{m_{1} + m_{2}}$

As $v_{2}$ is zero. $m_{2} > m_{1}, v_{1}^{'}$ is in the opposite direction.
$m_{1} = 1, m_{2} = A .$

$∴ | v_{1}^{'} | = \frac{(A - 1)^{2}}{(A + 1)^{2}} V_{1}$

The fraction of total energy retained is

$\frac{\frac{1}{2} m v^{' 2}}{\frac{1}{2} m v_{1}^{2}} = \frac{(A - 1)^{2}}{(A + 1)^{2}}$

Suggest Corrections

Similar questions

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

Q. Statement A : A neutron travelling with a velocity collides head on an atom of atomic mass number A at rest. The fraction of the total energy retained by neutron is

(\frac{A - 1}{A + 1})^{2}

Statement B : The kinetic energy conserves during an elastic collision

Q. A neutron travelling with a velocity

v

and kinetic energy

E

collides elastically head on with the nucleus of an atom of mass number

A

at rest. The fraction of total energy retained by the neutron is:

Q. A neutron travelling with a velocity

u

collides perfectly elastically head on with the nucleus of an atom of mass number A at rest. The fraction of total energy retained by neutron is

Q. A neutron with velocity

v

suffers head on elastic collision with the nucleus of an atom of mass number A at rest. The fraction of energy retained by the neutron is :

Join BYJU'S Learning Program

A neutron travelling with a velocity v and kinetic energy E has a perfectly elastic head-on collision with a nucleus of an atom of mass number A at rest. The fraction of total energy retained by the neutron is approximately

The correct option is A [A−1A+1]2 v′1=(m1−m2)v1+2m2v2m1+m2 As v2 is zero. m2>m1,v′1 is in the opposite direction. m1=1,m2=A. ∴|v′1|=(A−1)2(A+1)2V1 The fraction of total energy retained is 12mv′212mv21=(A−1)2(A+1)2