Atoms And Nuclei Question 400
Question: A radioactive nucleus (initial mass number A and atomic number Z emits 3 $ \alpha - $ particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
Options:
A) $ \frac{A-Z-8}{Z-4} $
B) $ \frac{A-Z-4}{Z-8} $
C) $ \frac{A-Z-12}{Z-4} $
D) $ \frac{A-Z-4}{Z-2} $
Show Answer
Answer:
Correct Answer: B
Solution:
- As a result of emission of 1 $ \alpha $ -particle, the mass number decreases by 4 units and atomic number decreases by 2 units. And by the emission of 1 positron the atomic number decreases by 1 unit but mass number remains constant.
$ \therefore $ Mass number of final nucleus $ =A-12 $ Atomic number of final nucleus $ =Z-8 $
$ \therefore $ Number of neutrons $ =(A-12)-(Z-8) $ $ =A-Z-4 $ Number of protons $ =Z-8 $
$ \therefore $ Required ratio $ =\frac{A-Z-4}{Z-8} $
