Question

A subatomic particle undergoes a one-dimensional elastic collision with an initially stationary atom. What percentage of the subatomic particle's initial kinetic energy is transferred to kinetic energy of the atom? (The mass of the atom is 1100 times the mass of the subatomic particle.)

Answer 1

let,

m2=1100*m1

and

by using law of conservation of momentum,

m1*u1+m2*u2=m1*v1+m2*v2

m1*u1+0=m1*v1+m2*v2

m1*u1=m1*v1+1100*m1*v2

u1=v1+1100*v2 ------(1)

and

u1-u2=v2-v1

u1-0=v2-v1

u1=v2-v1 ------(2)

from (1) and (2)

u1=v2-u1+1100*v2

2*u1=v2-1100*v2

===>

v2=-2*u1/1099

and

v1=-1099*u1/1101

and

K.E_initial=1/2*m1*u1^2

K.E_final=1/2*m2*v1^2

===>

K.E_final/K.E_initial=1/2*m2*v2^2/(1/2*m1*u1^2)

=m1*1100*(-2*u1/1101)^2/(m1*u1^2)

=1100*(2/1101)^2

=0.363% ---- answer