Looking for classes? Ksquare Career Institute, Bengaluru →
The radioisotope, tritium ($^{3}_{1}H$) has a half-life of 12.3 years. If the initial amount of tritium is 32 mg, how many milligrams of it would remain after 49.2 years :
A
1 mg
B
2 mg
C
4 mg
D
8 mg
Detailed Solution
Number of half lives: $n = \dfrac{49.2}{12.3} = 4$
Amount remaining $= N_0\left(\dfrac{1}{2}\right)^n = 32 \times \left(\dfrac{1}{2}\right)^4 = \dfrac{32}{16}$
$= 2$ mg
(32 mg $\rightarrow$ 16 $\rightarrow$ 8 $\rightarrow$ 4 $\rightarrow$ 2 mg.)
Amount remaining $= N_0\left(\dfrac{1}{2}\right)^n = 32 \times \left(\dfrac{1}{2}\right)^4 = \dfrac{32}{16}$
$= 2$ mg
(32 mg $\rightarrow$ 16 $\rightarrow$ 8 $\rightarrow$ 4 $\rightarrow$ 2 mg.)