In an alpha - decay,the kinetic energy of the | vedclass

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(B) In an $\alpha -$ decay,the reaction is given by: $_Z^AX 	o _{Z-2}^{A-4}Y + _2^4He$.The kinetic energy of the $\alpha -$ particle $(K_{\alpha})$ i

Vedclass · Accepted Answer

$100$

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(B) In an $\alpha -$ decay,the reaction is given by: $_Z^AX 	o _{Z-2}^{A-4}Y + _2^4He$.The kinetic energy of the $\alpha -$ particle $(K_{\alpha})$ is related to the $Q$ value of the reaction by the conservation of momentum and energy:$K_{\alpha} = \left( \frac{M_Y}{M_Y + M_{\alpha}} ight) Q$Here,$M_Y$ is the mass of the daughter nucleus,which is approximately $(A-4)$ and $M_{\alpha}$ is the mass of the $\alpha -$ particle,which is $4$.Substituting these values:$K_{\alpha} = \left( \frac{A-4}{(A-4) + 4} ight) Q$$K_{\alpha} = \left( \frac{A-4}{A} ight) Q$Given $K_{\alpha} = 48 \ MeV$ and $Q = 50 \ MeV$:$48 = \left( \frac{A-4}{A} ight) 	imes 50$$48A = 50(A - 4)$$48A = 50A - 200$$2A = 200$$A = 100$Thus,the mass number of the mother nucleus is $100$.

In an $\alpha -$ decay,the kinetic energy of the $\alpha -$ particle is $48 \ MeV$ and the $Q$ value of the reaction is $50 \ MeV$. The mass number of the mother nucleus is (assume that the daughter nucleus is in the ground state).

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