# In Which of the Following Systems Will the Radius of the First Orbit (N = 1) Be Minimum? - Physics

MCQ

In which of the following systems will the radius of the first orbit (n = 1) be minimum?

#### Options

• Hydrogen atom

• Deuterium atom

• Singly ionized helium

• Doubly ionized lithium

#### Solution

Doubly ionized lithium

For a hydrogen-like ion with Z protons in the nucleus, the radius of the nth state is given by

rn = (n^2a_0)/Z

Here , a_0 = 0.53 " pm"

For lithium,

Z = 3

Therefore, the radius of the first orbit for doubly ionised lithium will be minimum.

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 5 | Page 383