Nuclear Physics Practice Problems

  1. What is the net static electric charge on a metal sphere having an excess of +3 elementary charges?
  1. \(4.7 \times 10^{-18}\ \text{C}\)
  2. \(8.4 \times 10^{-19}\ \text{C}\)
  3. \(4.8 \times 10^{-19}\ \text{C}\)
  4. \(8.7 \times 10^{-19}\ \text{C}\)
Show Answer
The correct answer is C!

Charge is quantized in units of the elementary charge:

\(e \approx 1.60\times 10^{-19}\ \text{C}\)

For an excess of \(+3e\):

\(Q = 3e \approx 3(1.60\times 10^{-19}) = 4.8\times 10^{-19}\ \text{C}\)

 

  1. A hydrogen atom could have an electron energy level transition from \(n=2\) to \(n=3\) by absorbing a photon having an energy of how many eV?
  1. 1.89
  2. 2.04
  3. 2.25
  4. 2.87
Show Answer
The correct answer is A!

Hydrogen levels:

\(E_n = -\dfrac{13.6\ \text{eV}}{n^2}\)

Thus \(E_2=-3.40\ \text{eV}\) and \(E_3=-1.51\ \text{eV}\). The photon energy needed is:

\(\Delta E = E_3 – E_2\) \(\approx (-1.51)-(-3.40)\) \(=1.89\ \text{eV}\)

 

  1. Two solid metal blocks are placed in an insulated container. If there is a net flow of heat between the blocks, they must have different…
  1. Initial temperatures
  2. Specific heat values
  3. Melting points
  4. Heats of fusion
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The correct answer is A!

Heat flows spontaneously from higher to lower temperature until thermal equilibrium is reached (zeroth/second laws). Specific heat or melting point doesn’t determine the direction of heat flow; a temperature difference does.

 

  1. A p-type semiconductor is formed by adding impurities, which provide extra…
  1. Electrons
  2. Neutrons
  3. Photons
  4. Holes
Show Answer
The correct answer is D!

Acceptors create vacant states in the valence band that act as the majority carriers in p-type material.

 

  1. A student measures a current of 0.05 amperes through a p-type semiconductor sample with ohmic contacts. If the battery connections are reversed, what will the current through the semiconductor be (for the same applied voltage magnitude)?
  1. Less than 0.05 amperes
  2. Greater than 0.05 amperes
  3. The same
Show Answer
The correct answer is C!

For a uniform p-type sample with ohmic contacts (not a diode junction), \(I\propto V\) by Ohm’s law.

Reversing polarity just reverses the direction of hole drift. The magnitude stays \(0.05\ \text{A}\) for the same \(|V|\).

 

  1. What is the approximate binding energy of a helium nucleus that has a mass defect of \(5.2 \times 10^{-29}\ \text{kg}\)?
  1. \(4.6 \times 10^{-12}\ \text{J}\)
  2. \(4.6 \times 10^{-13}\ \text{J}\)
  3. \(4.7 \times 10^{-12}\ \text{J}\)
  4. \(4.7 \times 10^{-13}\ \text{J}\)
Show Answer
The correct answer is C!

Use mass–energy equivalence:

\(E=\Delta m\,c^2\) \(\approx (5.2\times 10^{-29}\ \text{kg})(3.00\times 10^8\ \text{m/s})^2\) \(\approx 4.68\times 10^{-12}\ \text{J}\) \(\approx 4.7\times 10^{-12}\ \text{J}\)

That’s about \(2.9\times 10^7 \text{ eV} \approx 29 \text{ MeV}\), consistent with He-4.

 

  1. Which particle cannot be accelerated by a cyclotron?
  1. Proton
  2. Neutron
  3. Electron
  4. α-particle
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The correct answer is B!

A cyclotron accelerates charged particles using an RF electric field and bends them with a magnetic field. Neutrons are neutral and don’t gain energy from the accelerating electric field.

 

  1. A 96 gram sample of a radioactive nuclide is placed in a container. After 12 minutes, only 6 grams of the sample remain undecayed. What is the half-life of the nuclide?
  1. 3 minutes
  2. 4 minutes
  3. 5 minutes
  4. 6 minutes
Show Answer
The correct answer is A!

Decay law:

\(N=N_0\left(\tfrac12\right)^{t/T_{1/2}}\)

Here, \(\tfrac{N}{N_0}=\tfrac{6}{96}=\tfrac{1}{16}=\left(\tfrac12\right)^4\), so \(\tfrac{t}{T_{1/2}}=4\).

With \(t=12 \text{ min}\):

\(T_{\tfrac{1}{2}}=\dfrac{12}{4}=3 \text{ min}\)

 

  1. What is the principal reason for using neutrons to bombard a nucleus?
  1. Neutrons have a relatively low atomic mass
  2. Neutrons can be easily accelerated
  3. Neutrons have a very high kinetic energy
  4. Neutrons are not repelled by the nucleus
Show Answer
The correct answer is D!

Because neutrons are uncharged, they don’t face a Coulomb barrier when approaching a positively charged nucleus, making nuclear reactions more probable at lower energies.

 

  1. What is the magnitude of the gravitational force between an electron and a proton separated by a distance of \(1.0 \times 10^{-10}\ \text{m}\)?
  1. \(1.0 \times 10^{-43}\ \text{N}\)
  2. \(1.0 \times 10^{-47}\ \text{N}\)
  3. \(2.0 \times 10^{-43}\ \text{N}\)
  4. \(3.05 \times 10^{-47}\ \text{N}\)
Show Answer
The correct answer is B!

At atomic separations, the gravitational pull is given by Newton’s law, \(F=G\tfrac{m_e m_p}{r^2}\).

Using \(G=6.67\times10^{-11}\), \(m_e=9.11\times10^{-31}\ \text{kg}\), \(m_p=1.67\times10^{-27}\ \text{kg}\), and \(r=1.0\times10^{-10}\ \text{m}\), we find \(m_e m_p\approx1.52\times10^{-57}\) and \(r^2=1.0\times10^{-20}\), giving \(F\approx1.0\times10^{-47}\ \text{N}\).

This reflects how much weaker gravity is than electric forces at atomic scales.

 

  1. A sphere has a net excess charge of \(-4.8 \times 10^{-19}\ \text{C}\). The sphere must have an excess of…
  1. 1 electron
  2. 1 proton
  3. 3 electrons
  4. 3 protons
Show Answer
The correct answer is C!

\(n=\dfrac{|Q|}{e}\) \(=\dfrac{4.8\times 10^{-19}}{1.60\times 10^{-19}}\) \(=3\)

The negative sign indicates excess electrons, not protons.

 

  1. An excited hydrogen atom returns to its ground state. Which of the following is a possible energy change for the atom?
  1. Loss of 10.20 eV
  2. Gain of 10.20 eV
  3. Loss of 11.70 eV
  4. Gain of 11.70 eV
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The correct answer is A!

Returning to ground means the atom loses energy by emitting a photon. The \(n=2\to 1\) transition is 10.20 eV. Gains aren’t possible when de-exciting, and 11.70 eV doesn’t correspond to an allowed Lyman transition.

 

  1. What is conserved during a collision between a proton and an electron?
  1. Energy
  2. Momentum
  3. Energy and momentum
  4. Neither energy nor momentum
Show Answer
The correct answer is C!

In an isolated system, total energy (including rest and kinetic) and total momentum are conserved in all collisions, elastic or inelastic.

 

  1. As the temperature of a surface increases, how does the rate of thermionic emission change?
  1. Electrons are emitted at a lower rate.
  2. Electrons are emitted at a higher rate.
  3. Protons are emitted at a lower rate.
  4. Protons are emitted at a higher rate.
Show Answer
The correct answer is B!

Thermionic emission increases rapidly with temperature. The emitted particles are electrons, not protons.