Nuclear Physics And Radioactivity Question 106
Question: A nucleus of mass number A, originally at rest, emits an a-particle with speed v. The daughter nucleus recoils with a speed
Options:
A) $ \frac{4v}{A-4} $
B) $ \frac{4v}{A+4} $
C) $ \frac{2v}{A+4} $
D) $ \frac{2v}{A-4} $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] The emission of an $ \alpha $ -particle from the atom of element reduces its atomic number by 2 and mass number by 4. Hence, the radioactive emission is as follows;
$ {Z}X^{A}{{\xrightarrow{\alpha -particle}}{Z-2}}{{Y}^{A-4}}+{}_{Z}He^{4}(\alpha \text{-}particle) $
Also from law of conservation of momentum, $ m\times 0=m_{y}v_{y}+{m_{\alpha }}{v_{\alpha }} $ $ =(A-4)v_{y}+4v $
$ \Rightarrow v_{y}=\frac{4v}{A-4} $
BETA
