Question

The half-life for rhodium $-101$ is $3.3$ years.
After $10$ years, about what fraction of some original amount of $rhodium-101$ would remain?

• A. One-third
• B. One-eighth
• C. One-tenth
• D. One-half
• E. One-fourth

Answer 1

The correct option is B One-eighth

Given : $T_{1/2}=3.3$ years

Time of observation, $t=10$ years

$\therefore$ Number of half lives, $n=\frac{t}{T_{1/2}}=\frac{10}{3.3}=3$

Amount of $Rh-$101 remains, $R=\frac{R_o}{2^n}$

$\therefore$ Fraction of original amount remaining, $\frac{R}{R_o}=\frac{1}{2^3}=\frac{1}{8}$