# The Radius of the Shortest Orbit in a One-electron System is 18 Pm. It May Be - Physics

MCQ

The radius of the shortest orbit in a one-electron system is 18 pm. It may be

• hydrogen

• deuterium

• He+

• Li++

#### Solution

Li++

The radius of the nth orbit in one electron system is given by
r_n = (n^2a_0)/Z

Here, a0 = 53 pm

For the shortest orbit,
n = 1

For hydrogen,
Z = 1

∴ Radius of the first state of hydrogen atom = 53 pm

For deuterium,
Z= 1

∴ Radius of the first state of deuterium atom = 53 pm

For He+,
Z = 2

∴ Radius of He+ atom =53/2 pm = 26.5 "pm"

For Li++,
Z = 3

∴ Radius of Li++ atom = 53/3 "pm" = 17.66"pm" ≈ 18 "pm"

The given one-electron system having radius of the shortest orbit to be 18 pm may be Li++.

The given one-electron system having radius of the shortest orbit to be 18 pm may be Li++.

Concept: The Line Spectra of the Hydrogen Atom
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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 10 | Page 383