Question

The half-life of radium is $1600$ years. A fraction $\frac{1}{16}$ of the sample will remain.

• A. $1600$ years
• B. $3200$ years
• C. $6400$ years
• D. $800$ years

Answer 1

The correct option is C $6400$ years

$t_{1/2}=1600k=\frac{\ln 2}{1600}\ln \left(\frac{A_o}{A_t}\right)=kt\ln 16=\frac{\ln 2}{1600}\times t\ln {\left(2\right)}^4=\frac{\ln 2}{1600}\times t4\ln 2=\frac{\ln 2}{1600}\times tt=1600\times 4t=6400years$