Question

Tritium, ${}_1^{3}H$ has a half-life of 12.26 years. A 5.00 mL sample of tritiated water has an activity of $2.40\times {10}^9$ cpm. How many years will it take for the activity to fall to $3.00\times {10}^8$ cpm?

• A. 6.13
• B. 12.26
• C. 24.52
• D. 36.78

Answer 1

Answer: (D)

36.78

As we know,
Activity is
$C=C_0{\left(\frac{1}{2}\right)}^y$

$(3.00\times {10}^8)=(2.40\times {10}^9){\left(\frac{1}{2}\right)}^y$

${\left(\frac{1}{2}\right)}^y=\left(\frac{1}{8}\right)={\left(\frac{1}{2}\right)}^3$

$y=3$

So it has completed three half time

$\frac{t}{t_{1/2}}=3$

$t=3\times t_{1/2}=36.78years$

So after 36.78 years, sample have activity of $(3.00\times {10}^8)$