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.

Question

Accepted Answer

Correct answer: B. (b) Given : Q=5.5 MeV Mass number of the nucleus A=220 Mass number of an -particle, M=4 units Mass number of daughter nucleus (M )=220-4=216 Q= (K .E )_ + (K .E )_y where (K.E) )_ is the kinetic energy of the -particle and (K.E) )_y is the kinetic energy of the daughter nuclei. If p and P denote momenta of the -particle and daughter nucleus respectively, then from eqn (i), we have Q= p^22m+ P^22M Since, momentum is conserved, thus P=p Q= p^22( 1m+ 1M)= p^22m(1+ mM) or Q= (K E )_ (1+ mM) or 5.5= (K .E )_ (1+ 4216) ∴ (K .E )_ = 5.5 216220=5.4 MeV

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

Solution

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