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Question: An energy of \(24.6eV\) is required to remove one of the electrons from a neutral helium atom. The e...

An energy of 24.6eV24.6eV is required to remove one of the electrons from a neutral helium atom. The energy (in eV) required to remove both the electrons from a neutral helium atom is-
(A) 38.2
(B) 49.2
(C) 51.8
(D) 79.0

Explanation

Solution

Hint
A helium atom contains two electrons. If one of the electrons is removed then the helium atom hydrogen like. In this situation, the Bohr has given a formula of energy of the electron in a hydrogen like atom.
According to the Bohr model of a hydrogen atom, the energy of an electron in nth orbit around hydrogen atom is given by
En=−13.6Z2n2eV{E_n} = - \dfrac{{13.6{Z^2}}}{{{n^2}}}eV…………… (1)
Here, ZZ is the atomic number of the hydrogen-like atom while n signifies the number of the orbit in which the electron is revolving.

Complete step by step solution
A helium atom contains two electrons. The amount of energy required to remove the outermost electron from an atom is known as ionization energy.
It is given that when one electron is removed from the helium atom, the amount of energy required is given as
E1=26.4eV{E_1} = 26.4eV
Now, we also want to remove the other electron from the other atom.
We notice that when one electron is removed from a helium atom it will become the hydrogen like atom.
Now, by using the Bohr model we can calculate the energy required to remove the second electron since now helium has become the hydrogen like upon removal of one electron. Therefore, we can use equation (1) where Z=2Z=2 for helium atom while n=1n=1 for ground state of the electron.
E2=13.6×41=54.4eV{E_2} = \dfrac{{13.6 \times 4}}{1} = 54.4eV
Hence the total amount of energy required to remove the two electrons from the helium atom is given as
E=E1+E2E = {E_1} + {E_2}
On substituting the values, we get
⇒E=24.6+54.4=79eV\Rightarrow E = 24.6 + 54.4 = 79eV
Hence option (D) is correct.

Note
The energy of the electrons revolving around the nucleus is taken as negative because it is bounded due to attractive forces between electrons and nucleus. The attractive forces are always taken as negative while the repulsive forces are taken as positive. The energy required to pull electrons out of the atom is positive.