Question

A radioactive element X decays by the sequence and with half life given below :
$X\underset{30min}{\overset{\alpha }{\to }}Y\underset{2days}{\overset{2\beta }{\to }}Z$
which of the following statements about this system are correct?

• A. After two hours, less than $10$% of the initial X is left
• B. An intermediate nuclide exists between Y and Z
• C. Atomic number of X and Z are same
• D. The mass number of Y is greater than X

Answer 1

Answer: (C)

Atomic number of X and Z are same

${}_Z^{A}X{\underset{30min}{\overset{\alpha }{\to }}}_{Z-2}^{A-4}Y{\underset{2days}{\overset{2\beta }{\to }}}_Z^{A-4}Z$

Thus atomic number of X and Z are same and mass number of Y is less than X and there is no intermediate state between Y and Z.
Let initially the amount of X is $N_0$.
After $30$ min it becomes $N_0/2$.

Then after 90 min it is: $N=\left(N_0/2\right)e^{-\lambda t}$
$N=0.49N_0$ where $\lambda t=\frac{0.693}{48\left(60\right)}90=0.021$