Question

The half-life of tritium, or hydrogen-3, is 12.32 years. After about 24.6 years, how much of a sample of tritium will remain unchanged?
A. 1/8
B. 1/4
C. 1/3
D. 1/2

Answer 1

Answer: The correct option is B.

Explanation: This is an example of radioactive decay and all the radioactive decay processes follow First order of kinetics.

Expression for the half life of first order kinetics is:

$t_{1/2}=\frac{0.693}{k}$

We are given:

$t_{1/2}=12.32years$

Putting in above equation, we get:

$12.32=\frac{0.693}{k}\\k=0.05625year^{-1}$

Expression to calculate the amount of sample which is unchanged is:

$N=N_oe^{-kt}$

where,

N = Amount left after time t

$N_o$ = Initial amount

k = Rate constant

t = time period

Putting value of k = 0.05625 and t = 24.6 in above equation, we get:

$N=N_oe^{-0.05625\times 24.6}$

$\frac{N}{N_o}=0.25$

The above fraction is the amount of sample unchanged and that is equal to $\frac{1}{4}$

Hence, the correct option is B.

Answer 2

The amount of the substance left after sometime, t, is given by the equation,
                                     At = (Ai) x e^-kt
where Ai is the initial amount and k is constant. From the given half-life,
                            At / Ai = 0.5 = e^-k(12.32)      ; k = 0.5626
Then, for the next set,
                             At/Ai = e^(-0.5626)x24.6 = 
Thus, the answer is letter B.