Step 1: Understand isotopes of hydrogen.
Hydrogen has three isotopes: protium (H), deuterium (D), and tritium (T). They differ only in neutron number, not in electronic configuration, so chemical bonding behavior is similar but with small isotopic effects.
Step 2: Internuclear distance concept.
Bond length in diatomic molecules like $H_2$ and $D_2$ depends mainly on electronic distribution. Since isotopes have identical electronic structures, the internuclear distance is essentially the same. Thus statement (1) is correct.
Step 3: Bond dissociation enthalpy comparison.
Due to isotopic effect, $D_2$ has slightly higher bond dissociation enthalpy than $H_2$ because heavier nuclei reduce vibrational zero-point energy. Hence statement (2) is incorrect.
Step 4: Relative abundance of isotopes.
Natural abundance follows:
\[
H \gt D \gt T
\]
Tritium is radioactive and extremely rare. Therefore statement (3) is incorrect.
Step 5: Neutron-to-proton ratio analysis.
For D: neutrons/protons = 1/1 = 1
For T: neutrons/protons = 2/1 = 2
Thus ratio is greater for T, not D. Hence statement (4) is incorrect.
Step 6: Final conclusion.
Only statement (1) is correct:
\[
\boxed{\text{Option (1)}}
\]