Atoms and Nuclei Questions and Answers

Answer: B

The SI unit of radioactivity is the becquerel (Bq).

One becquerel is one nuclear disintegration per second. It replaced the older curie, defined as the activity of one gram of radium-226, where 1 Ci = 3.7 x 10¹⁰ Bq.

The curie is a non-SI unit. The gray (J/kg) is the SI unit of absorbed dose, and the sievert is the unit of equivalent and effective dose. Both measure energy deposited in tissue, not the activity of the source.

Answer: C

The half-life is the time for activity to reduce to half its original value.

Radioactive decay is exponential, so the activity halves in each equal interval:

\[ \begin{aligned} A &= A_0 e^{-\lambda t} \\ t_{1/2} &= \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda} \end{aligned} \]

Because the decay is exponential, the activity never strictly reaches zero, so 'complete decay' and 'activity becomes zero' do not define any finite time. The reciprocal of the decay constant, 1/λ, is the mean life, which is about 1.44 times the half-life.

Answer: C

The time required is 3T.

If 87.5% has decayed, 12.5% remains, which is one-eighth. Each half-life halves the amount left:

\[ 100 \to 50 \to 25 \to 12.5\% \]

That is three halvings, \(\left(\tfrac{1}{2}\right)^{3} = \tfrac{1}{8}\), so the time is 3T. After T only 50% has decayed and after 2T 75%; 4T would leave 6.25%, a decay of 93.75%.