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mexx4u2nv
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
Alpha Particles, as p=m*v and the mass of an alpha particle is greater than the other options
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.
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.