Isotones are atoms of different elements that have the same number of neutrons but different numbers of protons. In other words, isotones have the same neutron number (\( A - Z \)) but different atomic numbers (\( Z \)).
Now, let's analyze the given options:
- Option A: \( _1^2 H \) and \( _1^3 H \)
- These are isotopes of hydrogen, not isotones. They have the same number of protons but different numbers of neutrons.
- Option B: \( _{79}^{197} {Au} \) and \( _{80}^{198} {Hg} \)
- These are isotones. Both have 118 neutrons (\( 197 - 79 = 118 \) and \( 198 - 80 = 118 \)), but different numbers of protons (79 for Au and 80 for Hg).
- Option C: \( _1^3 H \) and \( _2^3 He \)
- These are not isotones. They have the same number of nucleons (3), but different numbers of protons and neutrons.
- Option D: \( _{17}^{35} {Cl} \) and \( _{17}^{37} {Cl} \)
- These are isotopes of chlorine, not isotones. They have the same number of protons (17), but different numbers of neutrons.
- Option E: \( _{92}^{235} {U} \) and \( _{92}^{238} {U} \)
- These are isotopes of uranium, not isotones. They have the same number of protons (92) but different numbers of neutrons.
Therefore, the correct answer is:
\[
\boxed{\text{B) } _{79}^{197} {Au} \text{ and } _{80}^{198} {Hg}}
\]