If a proton and an anti-proton come close to each other and annihilate, how much energy will be released?

  • A
    $1.5 \times 10^{-10} \; J$
  • B
    $3 \times 10^{-10} \; J$
  • C
    $4.5 \times 10^{-10} \; J$
  • D
    None of these

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In the nuclear reaction,$_1H^2 + _1H^2 \to _0n^1 + _2He^3$. If the binding energy of deuteron is $2.23 \ MeV$ and the $Q$-value of the reaction is $3.27 \ MeV$,then the binding energy of $_2He^3$ is ......... $MeV$.

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The mass of a proton is $1.0073 \; u$ and that of a neutron is $1.0087 \; u$ ($u =$ atomic mass unit). The binding energy of ${ }_2^4 \text{He}$ is (Given: helium nucleus mass $\approx 4.0015 \; u$):

The energy equivalent to $1\,mg$ of matter in $MeV$ is

List-$I$ shows various functional dependencies of energy $(E)$ on the atomic number $(Z)$. Energies associated with certain phenomena are given in List-$II$. Choose the option that describes the correct match between the entries in List-$I$ to those in List-$II$.
List-$I$List-$II$
$(P) \ E \propto Z^2$$(1)$ energy of characteristic $x-$rays
$(Q) \ E \propto (Z-1)^2$$(2)$ electrostatic part of the nuclear binding energy for stable nuclei with mass numbers in the range $30$ to $170$
$(R) \ E \propto Z(Z-1)$$(3)$ energy of continuous $x-$rays
$(S) \ E$ is practically independent of $Z$$(4)$ average nuclear binding energy per nucleon for stable nuclei with mass number in the range $30$ to $170$
$(5)$ energy of radiation due to electronic transitions from hydrogen-like atoms

The energy in $MeV$ released due to the complete transformation of $1\, kg$ of mass into energy is $(c = 3 \times 10^8\, m/s)$:

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