Question

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

• A. $9$
• B. $100$
• C. $104$
• D. None of these

Answer 1

The correct option is B

$100$

Step 1: Given data

Given the kinetic energy, $KE=48MeV$

Q-value, $Q=50MeV$

Step 2: Formula used

We know that the kinetic energy of an alpha particle,

$KE=\frac{A-4}{A}\times Q$

Where $A$ is the mass number of the mother nucleus.

Step 3: Finding the value of $A$

$$\begin{gathered} KE=\frac{A-4}{A}\times Q \\ \Rightarrow 48=\frac{A-4}{A}\times 50 \\ \Rightarrow \frac{48}{50}=\frac{A-4}{A} \\ \Rightarrow 48A=50A-200 \\ \Rightarrow 2A=200 \\ \Rightarrow A=100 \end{gathered}$$

Thus, the mass of the mother nucleus is $100$.

Hence, option B is correct.