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13.Nuclei
medium
In a radioactive decay chain, ${ }_{90}^{232} Th$ nucleus decays to ${ }_{82}^{212} Pb$ nucleus. Let $N _\alpha$ and $N _\beta$ be the number of $\alpha$ and $\beta^{-}$particles, respectively, emitted in this decay process. Which of the following statements is (are) true?
$(A)$ $N _\alpha=5$ $(B)$ $N _\alpha=6$ $(C)$ $N _\beta=2$ $(D)$ $N _\beta=4$
A
$A,B$
B
$A,C$
C
$A,D$
D
$A,B,C$
(IIT-2018)
Solution
$\Delta Z =90-82=8$
$\Delta A =232-212=20$
${ }_{90} Th ^{232} \longrightarrow{ }_{82} Pb ^{212}$
Number of $\alpha$-particle $N _\alpha=\frac{20}{4}=5$
$\Delta Z =5 \times 2=10$
Number of $\beta$-particles $N_\beta=10-8=2$
Standard 12
Physics
