Atoms and Nuclei Questions and Answers

Answer: C

The keyed answer is \(n\tau T \ge 50 \times 10^{20}\) keVs/m\(^{3}\).

Lawson's criterion is a lower limit: for net energy from a thermonuclear plasma the product of density n, confinement time \(\tau\) and temperature T must be at least a certain value, so the sign must be \(\ge\), which removes options A and B (those give an upper limit).

The widely quoted threshold for deuterium-tritium fusion is a triple product of about \(3 \times 10^{21}\) keV s/m\(^{3}\), that is \(30 \times 10^{20}\). The keyed \(50 \times 10^{20}\) is the same order of magnitude and a stricter figure, and the value of \(150 \times 10^{20}\) in option D is five times the usual threshold. So among the four, option C is the only one with the right inequality and a size near the standard value. What could not be confirmed is a source quoting exactly \(50 \times 10^{20}\), so the figure rests on the key.

Answer: C

The energy liberated is about 4.03 MeV.

The reaction is \(d + d \rightarrow t + p\). The energy released is the mass lost multiplied by 931.5 MeV per u:

\[ \begin{aligned} \Delta m &= 2(2.014102) - (3.016049 + 1.007825) \\ &= 4.028204 - 4.023874 = 0.004330\ \text{u} \\ Q &= 0.004330 \times 931.5 = 4.03\ \text{MeV} \end{aligned} \]

The 200 volt option is not even an energy unit, and 100 MeV and 2.15 MeV do not follow from these masses; 2.15 MeV is roughly the binding energy of the deuteron.

Answer: B

Cathode rays are composed of electrons.

Cathode rays are streams of particles emitted from the negative electrode (cathode) of a discharge tube. In 1897 J.J. Thomson showed that they are deflected by electric and magnetic fields towards the positive side and measured their charge-to-mass ratio, proving them to be negatively charged particles: electrons.

Protons are positive and make up the anode (canal) rays, neutrons are uncharged and cannot be deflected, and whole atoms are not what streams from the cathode.

Answer: A

The neutron was discovered by James Chadwick.

In 1932 Chadwick showed that the penetrating radiation from beryllium struck by alpha particles consisted of neutral particles with a mass close to that of the proton. He received the Nobel Prize in Physics in 1935.

Rutherford discovered the nucleus and proposed that a neutral particle might exist, J.J. Thomson discovered the electron, and Marie Curie worked on radioactivity. None of them discovered the neutron.

Answer: B

Nuclear fusion occurs in the Sun.

In the Sun's core, at about 15 million degrees and enormous pressure, hydrogen nuclei fuse to form helium, releasing the energy that makes the Sun shine. All stars are powered in this way.

Satellites, Mercury and Venus are cold bodies compared with a star. They have neither the temperature nor the pressure needed to fuse nuclei. On Earth, fusion has been achieved only in hydrogen bombs and experimental reactors, while nuclear power stations use fission.

Answer: B

The commonly used moderator is heavy water.

A moderator slows down the fast neutrons released in fission so that they can cause further fission in uranium-235. Heavy water (deuterium oxide) does this while absorbing very few neutrons, which is why India's pressurised heavy water reactors use it; ordinary water and graphite are also used elsewhere.

Uranium is the fuel, cadmium absorbs neutrons and is used in control rods, and silicon has no role as a moderator.

Answer: A

Most of the fission energy appears as the kinetic energy of the fission fragments.

Of the roughly 200 MeV released when a uranium-235 nucleus splits, about 165-170 MeV is carried off as kinetic energy of the two fragment nuclei, which fly apart under their mutual electrostatic repulsion. The rest is shared among the neutrons (about 5 MeV), prompt gamma rays (about 7 MeV) and the later beta decay of the fragments.

The heat in a reactor comes mainly from the fragments slowing down in the fuel, so 'heat and light' describes what the kinetic energy becomes, not the form in which it is released.

Answer: D

The Sun gets its energy by fusion.

In the Sun's core, at about 15 million kelvin, hydrogen nuclei fuse into helium, mainly through the proton-proton chain. The mass of the helium formed is slightly less than that of the four protons that made it, and the difference appears as energy according to E = mc².

Fission (splitting heavy nuclei) powers nuclear reactors, not stars like the Sun. Radioactive decay and the photoelectric effect release far too little energy to account for the Sun's output.

Answer: A

One gram becomes 0.25 g after 140 days.

After each half-life the amount left halves. Going from 1 g to 0.25 g is a reduction to one-quarter, which takes two half-lives:

\[ \begin{aligned} N &= N_0 \left(\tfrac{1}{2}\right)^{n} \\ 0.25 &= 1 \times \left(\tfrac{1}{2}\right)^{n} \Rightarrow n = 2 \\ t &= 2 \times 70 = 140\ \text{days} \end{aligned} \]

70 days is a single half-life and leaves 0.5 g. 210 days is three half-lives and leaves 0.125 g, and 280 days is four half-lives and leaves 0.0625 g.

Answer: A

Charge quantization was verified by Millikan's oil drop experiment.

Millikan measured the charges on many tiny oil drops by balancing gravity against an electric field. Every charge he found was a whole-number multiple of one smallest value, about \(1.6 \times 10^{-19}\) C, showing that charge comes in discrete units of e.

The Franck-Hertz experiment demonstrated quantized energy levels in atoms, the Davisson-Germer experiment showed electron diffraction (the wave nature of electrons), and the Zeeman effect is the splitting of spectral lines in a magnetic field. None of them measures the unit of charge.