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} $

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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} $


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