Which one of the following statements is correct?

  • A
    The mass of the nucleus must be less than the sum of the masses of the constituent neutrons and protons.
  • B
    The mass of the nucleus must be equal to the sum of the masses of the constituent neutrons and protons.
  • C
    The mass of the nucleus must be greater than the sum of the masses of the constituent neutrons and protons.
  • D
    The mass of the nucleus must be equal to only the masses of the constituent neutrons or protons.

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How much energy is released when $1 \,g$ of hydrogen is converted into $0.993 \,g$ of helium?

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The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_b^p$ and the binding energy of a neutron be $E_b^n$ in the nucleus. Which of the following statement(s) is(are) correct?
$(A)$ $E_b^p - E_b^n$ is proportional to $Z(Z-1)$ where $Z$ is the atomic number of the nucleus.
$(B)$ $E_b^p - E_b^n$ is proportional to $A^{-1/3}$ where $A$ is the mass number of the nucleus.
$(C)$ $E_b^p - E_b^n$ is positive.
$(D)$ $E_b^p$ increases if the nucleus undergoes a beta decay emitting a positron.

$1 \text{ amu}$ is equal to

An alpha particle $\left({ }^{4} He\right)$ has a mass of $4.00300 \ amu$. $A$ proton has a mass of $1.00783 \ amu$ and a neutron has a mass of $1.00867 \ amu$. The binding energy of an alpha particle estimated from these data is closest to: (in $MeV$)

Explain the following forms and principles of energy:
$(a)$ The Equivalence of Mass and Energy
$(b)$ Nuclear Energy
$(c)$ The Principle of Conservation of Energy

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