A nucleus with mass number 220 initially at rest emits an alpha particle. If the Q value of reaction is 5.5 MeV . Calculate the value of kinetic energy of alpha particle

Step-by-step solution

Given, Q=5.5 MeV Mass number of nucleus =220 By conservation of linear momentum. M_ v_ =M_y v_y where, M_ , v_ are mass and velocity of -particle, and M_X v_X are mass and velocity of the daughter nuclei X . Since, Q=( KE )_ +( KE )_X Let Y be the nucleus with the mass number 220 and X be the daughter nuclei produced. Hence, we have ²²⁰ Y ²¹⁶ X+ ₄^2 Using conservation of linear momentum. M_ v_ =M_X v_X v_x= M_ v_ M_X aligned & From Eq. (i), Q= 1 2 M_ v_ ^2+ 1 2 M_X v_X^2 & 55= 1 2 M_ v_ ^2+ 1 2 M_ ^2 v_ ^2 M_x & 55