Question

The radioisotope, tritium (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?
(1) 1 mg
(2) 2 mg
(3) 4 mg
(4) 8 mg

Answer 1

Intial amount of tritium=32g

t1/2=12.3

since,49.2÷12.3=4

It means 4 t1/2's

12.3 12.3 12.3 12.3

32--------->16---------->8----------->4----------->2

hence,answer is 2g.

Answer 2

The milligrams of it that would remain after  49.2 years is 2 mg.

Explanation:

Formula used for first order kinetics:

$a=\frac{a_o}{2^n}$

where,

a = amount of reactant left after n-half lives = ?

$a_o$ = Initial amount of the reactant = 32 mg

n = number of half lives  = $\frac{\text {total time}}{\text{half life}}=\frac{49.2}{12.3}=4$

Putting values in above equation, we get:

$a=\frac{32}{2^4}$

$a=2mg$

Therefore, the milligrams of it that would remain after  49.2 years is 2 mg

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