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Suppose a nucleus of given mass number, initially at rest emits an $\alpha$-particle. How can I calculate kinetic energy of the $\alpha$-particle using no other data except the $Q$-value of the reaction? Now $Q$-value of a reaction is $$(m_{product} - m_{reactant}) c^2$$ But the masses(not mass numbers but exact masses) of product and reactant are not given, so I am stuck.

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  • $\begingroup$ I know that Q-value is the product of mass difference between product and reactant & velocity of light squared, but since I dont have the mass(not mass number, exact mass) of product or reactant, I am stuck $\endgroup$ – mayank budhwani Mar 29 '16 at 11:18
  • $\begingroup$ OK then; could you edit your question to include that information? $\endgroup$ – David Z Mar 29 '16 at 11:26
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The $Q$-value in physics is usually defined as $(M_{\text{final}} - M_{\text{initial}}) c^2 $

Use conservation of energy and conservation of momentum.

Now if you know what the parent atom is then you need to look up the data for the mass of the parent atom $M_P$, the mass of the daughter atom $M_D$ and the mass of a helium atom $m$.
Using the accurate value of the masses of the atoms will take care of the alpha not having any electrons.
It is often the case that using the nucleon (mass) number is accurate enough for everything except finding the $Q$-value..

Otherwise you should find the kinetic energy of the alpha particle in terms of $M_D, m, c$ and $Q$.

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