Question

A certain nuclei has a half life period of 30 min. If a sample containing 600 atoms is allowed to decay for 90 min, how many atoms will remain?

• A. 200 atoms
• B. 450 atoms
• C. 75 atoms
• D. 150 atoms

Answer 1

Answer: (C)

75 atoms

$t_{1/2}=30,T=90\therefore n=\frac{T}{t_{1/2}}=\frac{90}{30}=3$

$\therefore$ Number of half lives $=3$

We know that N $={\left(\frac{1}{2}\right)}^n{N}_0$

$\therefore$ N (Number of atoms left after) $={\left(\frac{1}{2}\right)}^3\times 600$ atoms.

$\therefore N=\frac{1}{8}\times 600=75atoms$