A nucleus of mass M + Delta m is at rest and | vedclass

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Question

(C) According to the law of conservation of energy,the total energy before decay equals the total energy after decay.The initial energy is the rest ma

Vedclass · Accepted Answer

$c \sqrt{\frac{2 \Delta m}{M}}$

Vedclass · Answer

(C) According to the law of conservation of energy,the total energy before decay equals the total energy after decay.The initial energy is the rest mass energy: $E_i = (M + \Delta m)c^2$.The final energy consists of the rest mass energy of the two daughter nuclei and their kinetic energy: $E_f = 2 	imes (\frac{M}{2})c^2 + 2 	imes (\frac{1}{2} 	imes \frac{M}{2} 	imes v^2)$.Equating $E_i = E_f$:$(M + \Delta m)c^2 = Mc^2 + \frac{M}{2}v^2$.Subtracting $Mc^2$ from both sides:$\Delta m c^2 = \frac{M}{2}v^2$.Solving for $v$:$v^2 = \frac{2 \Delta m c^2}{M} \Rightarrow v = c \sqrt{\frac{2 \Delta m}{M}}$.

$A$ nucleus of mass $M + \Delta m$ is at rest and decays into two daughter nuclei of equal mass $\frac{M}{2}$ each. The speed of light is $c$. The speed of the daughter nuclei is:

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