Question

Assertion :${}_Z{X}^4$ undergoes $2\alpha -decays,2\beta -decays$ (negative $\beta$), and $2\gamma -decays$. As a result, the daughter product is ${}_{z-2}{Y}^{A-B}$ Reason: In $\alpha -decay$, the mass number decreases by 4 unit and atomic number decreases by 2 unit. In $\beta -decay$ (negative $\beta$), the mass number remains unchanged and atomic number increases by 1 unit. In $\gamma -decay$, mass number and atomic number remain unchanged.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

We know that for a $\alpha$ decay: ${}_Z^{A}X{\to }_Z^{A}Y$
For 2 $\alpha$ decay: ${}_Z^{A}X{\to }_{Z-1}^{A}Y$
For a $\lambda$ decay: ${}_Z^{A}X{\to }_Z^A{Y}^{\ast }$
Thus, after decaying 2 $\alpha ,2\beta$ and 2 $\lambda$ decay , mass number becomes $A^{\prime }=A-2\left(4\right)=A-8$ and atomic number $Z^{\prime }=Z-2\left(2\right)+2\left(1\right)=Z-4+2=Z-2$
The daughter nucleus is ${}_{Z-2}^{A-8}Y$.