# The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10−11 m. What are the radii of the n = 2 and n = 3 orbits? - Physics

Numerical

The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10−11 m. What are the radii of the n = 2 and n = 3 orbits?

#### Solution

The radius of the innermost orbit of a hydrogen atom, r1 = 5.3 × 10−11 m.

Let r2 be the radius of the orbit at n = 2. It is related to the radius of the innermost orbit as:

"r"_2 = ("n")^2 "r"_1

= 4 × 5.3 × 10−11

= 2.12 × 10−10 m

For n = 3, we can write the corresponding electron radius as:

"r"_3 = ("n")^2 "r"_1

= 9 × 5.3 × 10−11

= 4.77 × 10−10 m

Hence, the radii of an electron for n = 2 and n = 3 orbits are 2.12 × 10−10 m and 4.77 × 10−10 m respectively.

Concept: Bohr’s Model for Hydrogen Atom
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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 12 Atoms
Exercise | Q 12.8 | Page 436
NCERT Class 12 Physics Textbook
Chapter 12 Atoms
Exercise | Q 8 | Page 436

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