MCQ

The energy of an atom (or ion) in its ground state is −54.4 eV. It may be

#### Options

hydrogen

deuterium

He

^{+}Li

^{++}

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#### Solution

He^{+}

The total energy of a hydrogen-like ion, having *Z* protons in its nucleus, is given by

`E = - (13.6Z^2)/(n^2)eV`

Here, *n* = Principal quantum number

For ground state,*n* = 1

∴ Total energy*, E* = - `13.6 Z^2 eV`

For hydrogen,*Z* = 1

∴ Total energy*, E *= - 13.6 eV

For deuterium,*Z* = 1

∴ Total energy*, E* = - 13.6 eV

For He^{+},*Z* = 2* *∴ Total energy*, E* = - 13.6×2^{2} = - 54.4 eV

For Li^{++},*Z* = 3

∴ Total energy*, E* = - 13.6×3^{2} = - 122.4 eV

Hence, the ion having an energy of −54.4 eV in its ground state may be He^{+}.

Concept: Introduction of Atoms

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