# How to calculate kinetic energy of emitted particle using Q-value?

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.

• 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 – mayank budhwani Mar 29 '16 at 11:18
• OK then; could you edit your question to include that information? – David Z Mar 29 '16 at 11:26

The $Q$-value in physics is usually defined as $(M_{\text{final}} - M_{\text{initial}}) c^2$
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 $m$.
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 $Q$.