Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# The Energy of an Atom (Or Ion) in Its Ground State is −54.4 Ev. It May Be - Physics

MCQ

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

•  hydrogen

• deuterium

• He+

• Li++

#### 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 = - 13.6×22 = - 54.4 eV

For Li++,
Z = 3
∴ Total energy, E = - 13.6×32 = - 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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#### APPEARS IN

HC Verma Class 11, Class 12 Concepts of Physics Vol. 2
Chapter 21 Bohr’s Model and Physics of Atom
MCQ | Q 9 | Page 383