Nuclear binding energy and mass defect Knowledge-Based Practice

Questions

1. 1.

   When the mass defect ($\Delta m$) of a nucleus is expressed in unified atomic mass units ($\text{u}$), which mathematical operation directly yields its total nuclear binding energy in megaelectronvolts ($\text{MeV}$)?

   • A) Multiplying $\Delta m$ by $931.5\text{ MeV/u}$
   • B) Dividing $\Delta m$ by $931.5\text{ MeV/u}$
   • C) Multiplying $\Delta m$ by the speed of light squared in meters per second
   • D) Dividing $\Delta m$ by the speed of light squared in meters per second
2. 2.

   Which expression correctly defines the mass defect ($\Delta m$) of a nucleus with atomic number $Z$ and mass number $A$, where $m_p$ is the mass of a free proton, $m_n$ is the mass of a free neutron, and $m_{\text{nucleus}}$ is the experimentally determined mass of the intact nucleus?

   • A) $\Delta m = m_{\text{nucleus}} - [Z \cdot m_p + (A - Z) \cdot m_n]$
   • B) $\Delta m = [Z \cdot m_p + A \cdot m_n] - m_{\text{nucleus}}$
   • C) $\Delta m = [Z \cdot m_p + (A - Z) \cdot m_n] - m_{\text{nucleus}}$
   • D) $\Delta m = [(A - Z) \cdot m_p + Z \cdot m_n] - m_{\text{nucleus}}$
3. 3.

   Which of the following statements correctly defines the nuclear binding energy of an atomic nucleus?

   • A) The energy released when an unstable nucleus undergoes spontaneous radioactive decay into a lighter daughter isotope.
   • B) The electrostatic potential energy required to overcome the attraction between orbital electrons and the positively charged nucleus.
   • C) The minimum energy required to completely disassemble an intact atomic nucleus into its individual, isolated nucleons.
   • D) The net thermal energy emitted when free electrons combine with bare protons to form neutral hydrogen atoms.
4. 4.

   Which statement correctly describes how the binding energy per nucleon relates to the stability of an atomic nucleus?

   • A) Nuclei with lower binding energy per nucleon are more stable because less energy was released during their formation.
   • B) The total binding energy determines stability directly, meaning larger nuclei are always more stable than smaller ones regardless of mass number.
   • C) A higher binding energy per nucleon indicates a more tightly bound nucleus, corresponding to greater overall nuclear stability.
   • D) Binding energy per nucleon remains constant across all stable isotopes because the nuclear force acts equally on all nucleons.
5. 5.

   Which of the following statements correctly explains why the actual mass of an intact atomic nucleus is always less than the sum of the individual masses of its separated constituent nucleons?

   • A) Excess nucleon mass is converted into electrical charge to neutralize the electrostatic repulsion between protons.
   • B) A fraction of the constituent mass is carried away as kinetic energy during spontaneous radioactive alpha decay.
   • C) The missing mass is converted into nuclear binding energy released when the nucleons bind together.
   • D) Neutrons shed a portion of their rest mass through weak interactions to transform into lighter neutral leptons.

Answers and step-by-step solutions appear after you finish the test.