Question

A free alpha particle and a free proton are separated by distance of 10 particle when at infinite separation is m and are released. The kinetic energy of alpha
Options:
-19 28.6 x 10 J
-19 9.2 x 10 J
-19 36.8 x 10 J
-19 12.5 x 10 J​

Answer 1

Kinetic energy of both α

-particle and proton

= Potential energy of two particles

(2e)(e) / 4πε0r

=2×(1.6×10−19)2×9×109 / 10−10

= 46.08×10−19

As initial momentum of two particles is zero, their final momentum must also be zero.

= Numerical value of momentum of each particle = p.

KE of proton = p²/ 2m=E(say)

Kinetic energy of α

-particle =p2²/ (4m)=E4

Total kinetic energy = E+ E/ 4=46.08×10−19J

= E=4/ 5×46×10−19J

=36.8×10−19J

hence, KE of α

-particle = 36.8×10−19 / 4

=29.2×10−19J

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