State what is meant by the binding energy of a nucleus.

In the nuclear reaction X + Y → Z + W, involving nuclides X, Y, Z and W, energy is released. Which is correct about the masses (M) and the binding energies (BE) of the nuclides?

In nuclear fission, a nucleus of element X absorbs a neutron (n) to give a nucleus of element Y and a nucleus of element Z.

X + n → Y + Z + 2n

What is $\frac{\text{magnitude of the binding energy per nucleon of Y}}{\text{magnitude of the binding energy per nucleon of X}}$ and $\frac{\text{total binding energy of Y and Z}}{\text{total binding energy of X}}$?

Show that the energy released in the β^– decay of rhodium is about 3 MeV.

Show that the energy released in the reaction is about $180 \mathrm{MeV}$.

The binding energy per nucleon of ${}_4^{11}Be$ is 6 MeV. What is the energy required to separate the nucleons of this nucleus?

A.  24 MeV

B.  42 MeV

C.  66 MeV

D.  90 MeV

Carbon-14 (C-14) is a radioactive isotope which undergoes beta minus (β^–) decay to the stable isotope nitrogen-14 (N-14). Energy is released during this decay. Explain why the mass of a C-14 nucleus and the mass of a N-14 nucleus are slightly different even though they have the same nucleon number.

The positions of stable nuclei are plotted by neutron number n and proton number p. The graph indicates a dotted line for which n = p. Which graph shows the line of stable nuclides and the shaded region where unstable nuclei emit beta minus (β^-) particles?

Identify particle X.

Calculate the binding energy per nucleon for uranium-238.

Draw, on the axes, a graph to show the variation with nucleon number $A$ of the binding energy per nucleon, $\frac{\text{BE}}{A}$. Numbers are not required on the vertical axis.

Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.

Draw, on the axes, a graph to show the variation with nucleon number $A$ of the binding energy per nucleon, $\frac{\text{BE}}{A}$. Numbers are not required on the vertical axis.

Identify, with a cross, on the graph in (a)(ii), the region of greatest stability.

When an alpha particle collides with a nucleus of nitrogen-14 $\left({}_7^{14}\mathrm{N}\right)$, a nucleus X can be produced together with a proton. What is X?

A. ${}_8^{18}\mathrm{X}$

B. ${}_8^{17}\mathrm{X}$

C. ${}_9^{18}\mathrm{X}$

D. ${}_9^{17}\mathrm{X}$

What is the energy equivalent to the mass of one proton?

A.  9.38 × (3 × 10⁸)² × 10⁶ J

B.  9.38 × (3 × 10⁸)² × 1.6 × 10^–19 J

C.  $\frac{9.38\times {10}^8}{1.6\times {10}^{-19}}$J

D.  9.38 × 10⁸ × 1.6 × 10^–19 J

The mass of nuclear fuel in a nuclear reactor decreases at the rate of $8 \mathrm{mg}$ every hour. The overall reaction process has an efficiency of $50 \%$. What is the maximum power output of the reactor?

A.  $100 \mathrm{MW}$

B.  $200 \mathrm{MW}$

C.  $100 \mathrm{GW}$

D.  $200 \mathrm{GW}$

Calculate the ratio $\frac{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{alpha} \mathrm{particle}}{\mathrm{kinetic} \mathrm{energy} \mathrm{of} \mathrm{thorium} \mathrm{nucleus}}$.

What is the definition of the unified atomic mass unit?

A.  $\frac{1}{12}$ the mass of a neutral atom of carbon-12

B.  The mass of a neutral atom of hydrogen-1

C.  $\frac{1}{12}$ the mass of a nucleus of carbon-12

D.  The mass of a nucleus of hydrogen-1

The rest mass of the helium isotope ${}_2^3\text{He}$ is m.

Which expression gives the binding energy per nucleon for ${}_2^3\text{He}$?

A. $\frac{(2m_p+m_n+m)c^2}{3}$

B. $\frac{(2m_p+m_n-m)c^2}{3}$

C. $(2m_p+m_n+m)c^2$

D. $(2m_p+m_n-m)c^2$

Show that the energy released in the reaction is about $180 \mathrm{MeV}$.

Uranium-235 $\left({}_{92}{}^{235}\text{U}\right)$ is used as a nuclear fuel. The fission of uranium-235 can produce krypton-89 and barium-144.

Determine, in MeV and using the graph, the energy released by this fission.

During the nuclear fission of nucleus X into nucleus Y and nucleus Z, energy is released. The binding energies per nucleon of X, Y and Z are $B_{\text{X}}$ , $B_{\text{Y}}$ and $B_{\text{Z}}$ respectively. What is true about the binding energy per nucleon of X, Y and Z?

A.  $B_{\text{Y}}$ > $B_{\text{X}}$ and $B_{\text{Z}}$ > $B_{\text{X}}$

B.  $B_{\text{X}}$ = $B_{\text{Y}}$ and $B_{\text{X}}$ = $B_{\text{Z}}$

C.  $B_{\text{X}}$ > $B_{\text{Y}}$ and $B_{\text{X}}$ > $B_{\text{Z}}$

D.  $B_{\text{X}}$ = $B_{\text{Y}}$ + $B_{\text{Z}}$

Uranium-235 (${}_{92}{}^{235}\text{U}$) is used as a nuclear fuel. The fission of uranium-235 can produce krypton-89 and barium-144.

Determine, in MeV and using the graph, the energy released by this fission.

The mass of a nucleus of iron-56 (${}_{26}{}^{56}\text{Fe}$) is M.

What is the mass defect of the nucleus of iron-56?

A.  M − 26m_p − 56m_n

B.  26m_p + 30m_n − M

C.  M − 26m_p − 56m_n − 26m_e

D.  26m_p + 30m_n + 26m_e − M

Which property of a nuclide does not change as a result of beta decay?

A. Nucleon number

B. Neutron number

C. Proton number

D. Charge

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

The plutonium nucleus is at rest when it decays.

Calculate the ratio $\frac{\text{kinetic energy of alpha particle}}{\text{kinetic energy of uranium}}$.

Show that the energy released in this decay is about 6 MeV.

Show that the energy released in this decay is about 6 MeV.

A neutron is absorbed by a nucleus of uranium-235$\left({}_{92}{}^{235}\text{U}\right)$. One possible outcome is the production of two nuclides, barium-144$\left({}_{56}{}^{144}\text{Ba}\right)$ and krypton-89$\left({}_{36}{}^{89}\text{Kr}\right)$.

How many neutrons are released in this reaction?

A.  0

B.  1

C.  2

D.  3