Question

A radioactive element decays as:

Which of the following statements about this decay process is/are 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 Y is the same
• D. Mass number of X and Y is the same

Answer 1

Answer: (C), (D)

The correct options are
C Atomic number of X and Y is the same
D Mass number of X and Y is the same

Given
$X\stackrel{\alpha }{⟶}Y\stackrel{\beta }{⟶}Z$
i.e
${}_Z^{A}X\stackrel{\alpha }{⟶}{}_{Z-2}^{A-4}Y\stackrel{\beta }{⟶}{}_{Z-4}^{A-4}Z$

A) $X\to \frac{X}{2}⟶\frac{X}{4}⟶\frac{X}{6}⟶\frac{X}{8}⟶\frac{X}{16}$

$\frac{X}{16}$ < 10
So, this is a true statement

B) Y is the product of X and is also getting consumed to produce Z. So, it is a true statement

C) As ${}_Z^{A}X\stackrel{\alpha }{⟶}{}_{Z-2}^{A-4}Y$ is the alpha decay then there is diffrence in atomic number of X and Y as shown. So, the statement is incorrect.

D) As ${}_Z^{A}X\stackrel{\alpha }{⟶}{}_{Z-2}^{A-4}Y$ is the alpha decay then there is diffrence in mass number of X and Y as shown. So, the statement is incorrect.