Question

For the same kinetic energy, the momentum shall be maximum for which one of these:
1. Electron
2. Alpha particles
3. Neutron
4. Deuteron
5. Proton
6. Gamma particles

Answer 1

Alpha Particles, as p=m*v and the mass of an alpha particle is greater than the other options

Answer 2

K=mv^2/2
this can be written as :
K=m^2*v^2/2m
which can be written in terms of momentum as:
K=p^2/2m
Rearranging the terms :
p=sqrt(2Km)

For given K, the larger the mass of the particle the greater will be its p
Hence "alpha particle" will have greater momentum.

NOTE: However the converse is not true- For given momentum the lighter particle will have greater Kinetic energy as can be seen from the formula: K=p^2/2m
This is contrary to what one may expect.

Answer 3

Kinetic energy is given by
\[KE = \frac{ 1 }{ 2 } m v^2\] rearrange to to find v, since KE is the same for all:\[v = \sqrt{\frac{ 2 \times KE }{m}}\]and insert this into the formula for momentum, p = mv
\[\rho = m v = m \sqrt{\frac{ 2 \times KE }{m}}\] and square the m and bring it under the square root sign, cancel off an m, to get:
\[\rho = \sqrt{2 \times KE \times m}\]
Since 2*KE is the same for all the particles, momentum is proportional to the square root of mass - the larger the mass of the particle, the higher the momentum.