Question

A radioactive element decays as,
$X\underset{t_{1/2}=30min}{\overset{\alpha decay}{\to }}Y\underset{t_{1/2}=2days}{\overset{(-2\beta )\beta decay}{\to }}Z$
which of the following statements about this decay process incorrect?

• A. After two hours, less than $10$% of the initial $X$ is left
• B. Maximum amount of $Y$ present at any time before $30$ min is less than $50$% of the initial amount of $X$
• C. Atomic number of $X$ and $Z$ are same
• D. The mass number of $Y$ is greater than $X$

Answer 1

Answer: (D)

The mass number of $Y$ is greater than $X$

${}_Z^{A}X\underset{\alpha -decay}{\overset{t_{1/2}=30min}{\to }}{}_{Z-2}^{A-4}Y\underset{(-2\beta )\beta -decay}{\overset{t_{1/2}=2days}{\to }}{}_Z^{A-4}Z$

$\Rightarrow$Atomic number of X and Z are same.

$\Rightarrow$No. of half life of X in 2 hours = 4.

Remaining amount = ${\left(\frac{1}{2}\right)}^4\times \left(original\right)$.

= 0.0625

$\therefore$only 6.25% remains.

$\Rightarrow$Maximum amount of y present at any time before 30 min is less than 50% of the initial amount of X.

$\therefore$incorrect statement : "The mass number of Y is greater than X".