Q104 / 180 · AIIMS 2015 · Physics

The half-life of radium is 1600 years. What is the fraction of sample undecayed after 6400 years?

  • Correct answer
    A
    $\frac{1}{16}$
  • B
    $\frac{1}{4}$
  • C
    $\frac{1}{8}$
  • D
    $\frac{1}{24}$

Solution

Half-life, $T=1600$ years Time of decay, $t=6400$ years Number of half-lives, $n=\frac{t}{T}=\frac{6400}{1600}=4$ Fraction undecayed $=\frac{N}{N_0}=\left(\frac{1}{2}\right)^n=\left(\frac{1}{2}\right)^4=\frac{1}{16}$

Hence, the correct answer is option: 'A'.

Relevant Questions