Question

If ionisation potential for hydrogen atom is 13.6 eV, then ionisation potential for $He^+$ will be

• A. 54.4 eV
• B. 6.8 eV
• C. 13.6 eV
• D. 24.5 eV

Answer 1

The Correct Option is A

The ionisation potential of an atom or ion is the energy required to remove an electron from the outermost shell when it is in its ground state.

To determine the ionisation potential for He^+, we can use the formula for the energy of a hydrogen-like atom, which is given by:

E_n = -13.6 \times \frac{Z^2}{n^2} \, \text{eV}

where:

• Z is the atomic number.
• n is the principal quantum number of the orbit.
• -13.6 \, \text{eV} is the energy for hydrogen (which is a hydrogen-like atom with atomic number 1) in its ground state.

For He^+ (a singly ionised helium ion), Z = 2, and we are interested in the ionisation energy from the ground state, so n = 1.

Substituting these values in:

E_1 = -13.6 \times \frac{(2)^2}{(1)^2} \, \text{eV}

E_1 = -13.6 \times 4 \, \text{eV} = -54.4 \, \text{eV}

The negative sign indicates the energy is required to overcome the attraction between the electron and the nucleus. Thus, the ionisation energy is 54.4 \, \text{eV}.

Therefore, the ionisation potential for He^+ is 54.4 eV, which matches the given correct option.