Question

The half-life of a radioisotope is one week. How much of the substance is left after a $28$-day period?

• A. $1/2$
• B. $1/4$
• C. $1/8$
• D. $1/16$
• E. $1/32$

Answer 1

Answer: (D)

$1/16$

Given : Half life $T=7days$, Time $t=28days$

By, $\frac{N}{N_0}={\left(\frac{1}{2}\right)}^{\frac{t}{T}}$ , where $N=$ substance left after time t, and $N_0=$initial amount of substance

$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^{\frac{28}{7}}$

$\frac{N}{N_0}={\left(\frac{1}{2}\right)}^4$

$N=N_0\times \frac{1}{16}$