Nuclear Chemistry — Practice Quiz

A Chemistry cheat sheet for Nuclear Chemistry — every key formula with its symbols defined — plus a medium-level practice quiz to test recall.

Practice quiz

1. In the first-order rate law for nuclear decay, $\ln\frac{N_t}{N_0} = -kt$, what does the term $N_t$ represent?

   • The initial amount of radioactive substance.
   • The decay constant of the substance.
   • The amount of radioactive substance remaining at time $t$.
   • The half-life of the substance.

   Answer: The amount of radioactive substance remaining at time $t$.

2. A radioactive isotope has a half-life of $20$ years. Calculate its decay constant $k$.

   • $0.0347 \text{ years}^{-1}$
   • $0.693 \text{ years}^{-1}$
   • $13.86 \text{ years}^{-1}$
   • $20 \text{ years}^{-1}$

   Answer: $0.0347 \text{ years}^{-1}$

3. If the decay constant $k$ for a radioactive substance is $0.05 \text{ s}^{-1}$, what is its half-life $t_{1/2}$?

   • $0.05 \text{ s}$
   • $13.86 \text{ s}$
   • $0.693 \text{ s}$
   • $20 \text{ s}$

   Answer: $13.86 \text{ s}$

4. In Einstein's mass-energy equation, $E = mc^2$, what does the symbol $c$ represent?

   • The speed of sound.
   • The speed of light in a vacuum.
   • The decay constant.
   • The amount of energy released.

   Answer: The speed of light in a vacuum.

5. A sample initially contains $100 \text{ g}$ of a radioactive isotope. If its decay constant $k$ is $0.02 \text{ day}^{-1}$, how much of the isotope will remain after $30$ days?

   • $40.5 \text{ g}$
   • $54.9 \text{ g}$
   • $60.0 \text{ g}$
   • $80.0 \text{ g}$

   Answer: $54.9 \text{ g}$

6. A radioactive sample initially had $200 \text{ Bq}$ of activity. After some time, its activity dropped to $50 \text{ Bq}$. If the decay constant $k$ is $0.01 \text{ min}^{-1}$, how much time has passed?

   • $69.3 \text{ min}$
   • $100.0 \text{ min}$
   • $138.6 \text{ min}$
   • $200.0 \text{ min}$

   Answer: $138.6 \text{ min}$

7. Calculate the energy released (in Joules) if $1.0 \times 10^{-3} \text{ kg}$ of mass is converted into energy. Use $c = 3.00 \times 10^8 \text{ m/s}$.

   • $3.0 \times 10^5 \text{ J}$
   • $9.0 \times 10^{13} \text{ J}$
   • $1.0 \times 10^{-3} \text{ J}$
   • $9.0 \times 10^{16} \text{ J}$

   Answer: $9.0 \times 10^{13} \text{ J}$

8. According to the formula $k = \frac{0.693}{t_{1/2}}$, what happens to the decay constant $k$ if the half-life $t_{1/2}$ of a radioactive isotope increases?

   • $k$ increases.
   • $k$ decreases.
   • $k$ remains unchanged.
   • $k$ becomes zero.

   Answer: $k$ decreases.

9. A sample of a radioactive element has an initial mass of $80 \text{ mg}$ and a half-life of $10$ hours. What mass of the element will remain after $30$ hours?

   • $40 \text{ mg}$
   • $20 \text{ mg}$
   • $10 \text{ mg}$
   • $5 \text{ mg}$

   Answer: $10 \text{ mg}$

10. The equation $E = mc^2$ is most directly applicable to which of the following phenomena?

    • Chemical reactions involving combustion.
    • The motion of planets around the sun.
    • Nuclear fission and fusion reactions.
    • The expansion of gases in a container.

    Answer: Nuclear fission and fusion reactions.