Question

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

• 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. All of the above

Answer 1

Answer: (D)

All of the above

$X\stackrel{\alpha }{\underset{30min}{⟶}}Y\stackrel{2\beta }{\underset{2days}{⟶}}Z$
After 2hr (4 half time of X), rameining molecules of X $=N/2^4=N/16$
so remaining % of $X$ are $6.25$ %
Before 3o min, less than half of molecules of X dissociates so less than 50% forms.
Also,
${}_Z^{A}X{\stackrel{\alpha }{\underset{30min}{⟶}}}_{N-2}^{A-4}Y{\stackrel{2\beta }{\underset{2days}{⟶}}}_N^{A-4}Z$
So X and Z have same atomic no but different masses so they are isotopes.