Question

A proton (mass 1.67 x ${10}^{-27}$ kg) on striking a neutron (mass nearly equal to the proton ) forms a deutron. What would be the velocity of the deutron if it is formed by a proton moving left with a velocity of 7.0 x 10${}^6$ m/s and a neutron moving right with a velocity of 4.0 x 10${}^6$ m/s

Answer 1

Given,

$mass=1.67\times {10}^{27}kg,$ Velocty of proton is $7.0\times {10}^{6}m/s$ Velocity of neutron is $4.0\times {10}^{6}m/s$

So, BY the conservation of momentum, let m be the mass of the proton, so 2m is the mass of the deuteron.

Initially, the momentum of the proton is $-m\times 7\times {10}^{6}kgm/s$

Initial momentum of the neutron is $+m\times 4\times {10}^{6}kgm/s$

so, total momentum is $-m\times {10}^{6}kgm/s$

Now, after the attachment of the mass 2m,

Let v be the velocity of the deuteron,

Then $2mv=-m\times 3\times {10}^6$

Canceling m then e get,

$v=-1.5\times {10}^{6}m/s$