Nuclear Chemistry Questions and Answers

Answer: C

¹⁴C decays by β decay and ¹⁴O by positron emission.

¹⁴C has 6 protons and 8 neutrons, more neutrons than the stable ¹²C. A neutron-rich nucleus moves towards stability by turning a neutron into a proton and emitting an electron (β⁻), giving ¹⁴N.

¹⁴O has 8 protons and only 6 neutrons, so it is proton-rich. It turns a proton into a neutron and emits a positron (β⁺), also giving ¹⁴N.

The options naming a single mode for both nuclei ignore that they lie on opposite sides of the band of stability, and option D reverses them.

Answer: D

The radioactive isotope of hydrogen is tritium.

Hydrogen has three natural isotopes: protium (one proton, no neutron), deuterium (one proton and one neutron) and tritium (one proton and two neutrons). Protium and deuterium are stable, but tritium is radioactive: it decays by beta emission to helium-3 with a half-life of about 12.3 years.

Helium is a different element, not an isotope of hydrogen, and it is also the product of tritium's decay. Protium and deuterium are hydrogen isotopes, but stable ones.

Answer: A

The fragments are ⁹⁴Kr + ¹⁴⁰Ba + 2n.

A nuclear equation must balance both mass number and atomic number. Neutron capture gives ²³⁶U (Z = 92):

\[ \begin{aligned} \text{mass: } & 235 + 1 = 94 + 140 + 2 = 236 \\ \text{charge: } & 92 = 36\ (\mathrm{Kr}) + 56\ (\mathrm{Ba}) \end{aligned} \]

With ¹³⁹Ba and two neutrons, or ¹⁴⁰Ba and one neutron, the mass numbers add to 235, one short. Xenon (Z = 54) with krypton gives a total charge of 90, not 92.

Answer: B

The measured activity is the sum of the activity of each isotope.

A counter registers every decay event that reaches it, whichever nucleus it comes from. In a mixture, the two isotopes decay independently, so the observed count rate is the sum of the two contributions, each decaying with its own half-life: A = λ₁N₁ + λ₂N₂.

This additivity is what allows a composite decay curve to be resolved into its components, by subtracting the long-lived contribution extrapolated back from late times. A difference, product or ratio of activities has no physical meaning as a count rate.

Answer: D

The isotope used for radiocarbon dating (the paper's 'radiating') is ¹⁴C.

¹⁴C is produced in the upper atmosphere by neutrons acting on nitrogen, enters living organisms through CO₂, and decays by β emission with a half-life of about 5730 years. After death the intake stops, so the remaining ¹⁴C activity measures the time elapsed.

¹²C and ¹³C are stable and cannot be used for dating, though ¹³C is used in NMR and in isotope-ratio studies. ¹¹C is radioactive but has a half-life of only about 20 minutes, which suits positron emission tomography, not dating.

Answer: B

The product is radium-228, ₈₈Ra²²⁸.

An alpha particle is a helium nucleus with two protons and two neutrons. Emitting one lowers the atomic number by 2 and the mass number by 4:

\[ \begin{aligned} &{}_{90}\mathrm{Th}^{232} \\ &\rightarrow {}_{88}\mathrm{Ra}^{228} + {}_{2}\mathrm{He}^{4} \end{aligned} \]

Atomic number 88 is radium. This is the first step of the thorium decay series. ₉₀Th²³¹ keeps the atomic number and loses only one mass unit, which is not alpha decay. Radium-223 and radium-226 have the right element but the wrong mass number; radium-226 belongs to the uranium-238 series.

Answer: B

The SI unit of radioactivity is the becquerel.

One becquerel (Bq) is one disintegration per second. It replaced the curie, the older non-SI unit equal to 3.7 × 10¹⁰ Bq.

The rad and the gray measure absorbed dose of radiation, energy deposited per kilogram of matter, not the activity of a source; the gray is the SI unit of absorbed dose and the rad its older counterpart.

Answer: C

After two half-lives the activity falls to 1/4 of the initial activity.

Each half-life halves the activity:

\[ \begin{aligned} A &= A_{0}\left(\tfrac{1}{2}\right)^{n} \\ &= A_{0}\left(\tfrac{1}{2}\right)^{2} = \tfrac{1}{4}A_{0} \end{aligned} \]

One half is the value after a single half-life. One third and one sixth come from treating the decay as linear or dividing by the number of half-lives, which is not how exponential decay works.

Answer: B

The scintillator crystal is sodium iodide.

A single crystal of sodium iodide doped with thallium, NaI(Tl), is the standard scintillator for gamma-ray detection. Iodine's high atomic number gives efficient absorption of gamma rays, and the crystal converts the absorbed energy into flashes of light, which a photomultiplier tube turns into electrical pulses.

Sodium nitrate, sulphate and carbonate are not used as scintillators: they lack the high atomic number and the light-emitting activator centres needed.

Answer: C

At radioactive equilibrium the relative amounts are constant irrespective of time.

Equilibrium (secular or transient) is reached when the daughter is being formed and decaying at rates linked to the parent's decay, so the ratio of daughter to parent atoms settles to a constant value. In secular equilibrium the activities are equal; in transient equilibrium the ratio is fixed by the two decay constants.

Before equilibrium the ratio does change, which is the trap in options A, B and D, but once equilibrium is attained it is fixed.