A molecule of hydrogen contains two protons and two electrons. The nuclear force between these two protons is always neglected while discussing the behaviour of a hydrogen molecule. Why?

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Solution

Inside the nucleus, two protons exert nuclear force on each other. These forces are short-ranged (a few fm), strong and attractive forces. They also exert electrostatic repulsive force (long-ranged). While discussing the behaviour of a hydrogen molecule, the nuclear force between the two protons is always neglected. This is because the separation between the two protons in the molecule is $~$ 70 pm which is much greater than the range of the nuclear force.

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A neutral hydrogen molecule has two protons and two electrons. If one of the electrons is removed we get a hydrogen molecular ion $(H_{2}^{+})$ . In the ground state of $H_{2}^{+}$ the two protons are separated by roughly $1.5$ $A^{o}$ and the electrons is roughly $1$ $A^{o}$ from each proton. The potential energy of the system is :

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