Question

What is binding energy of the Hydrogen nucleus?
(A) Zero
(B) 13.6eV
(C) More than 13.6eV
(D) Infinite.

Answer 1

Hint: Binding energy is related to the number of nucleons present in the nucleus. More the number of nucleons more will be binding energy.

Complete step by step answer:
Binding energy is the amount of energy required to separate a particle from a system. Binding energy is applicable when atoms/ions are bound in the crystal. It is also applicable to the subatomic particles i.e. electrons which are bound to the nucleus of the atom.
There are different types of binding energy.
1.) Electron binding energy
2.) Atomic binding energy
3.) Nuclear binding energy
4.) Bond dissociation energy
5.) Quantum binding energy
6.) Gravitational binding energy

Binding energy is directly proportional to mass: A system which is at ground state carries less energy as compared to the system which is in an excited state. Mass of the system in ground state is less when compared to the mass of the excited state.
Now let’s understand this with an example. Taking He which has atomic mass 4 and atomic number is equal to 2. We know that there are 2 protons and 2 neutrons in the nucleus. If we check individual mass of these subatomic particles,
\[{\text{Mass of proton = 1}}{\text{.00727647 amu}}\].
\[{\text{n = 1}}{\text{.00866440 amu}}\].

So after calculating theoretically the sum of masses of two protons and 2 neutrons is equal to 4.0318874 amu. But practically the atomic mass was found to be 4.00150608 amu. We can see that the predicted atomic mass is greater than actual mass. The difference between these two masses is known as mass defect. The mass defect is converted to energy when the nucleus is formed.
We can use Einstein’s equation to calculate the energy released. Einstein’s equation \[{\text{E = m}}{{\text{c}}^{\text{2}}}\]

In the case of a Hydrogen atom, it has only 1 proton and zero neutrons. In this case the proton is already separated from other nucleons. So, energy is not released in this case. Therefore, binding energy is equal to zero. So, the correct answer is “Option A”.

Note: The binding energy is always a positive number as energy is required to separate the nucleons. Binding energy of protons and neutrons is million times greater than the binding energy of electrons in an atom.