The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11}\ \text{m}$. What is the radius of the orbit in the second excited state?

$r_3 = 9\,r_1 = 4.77\times10^{-10}\ \text{m}$ (second excited state is $n=3$).

CBSE Class 12 · 2010 · Modern PhysicsVery Short Answer

The radius of the innermost electron orbit of a hydrogen atom is

5.3 \times 1 0^{- 11} m

. What is the radius of the orbit in the second excited state?

Answer: $r_{3} = 9 r_{1} = 4.77 \times 1 0^{- 10} m$ (second excited state is $n = 3$ ).

The radius of the

n^{th}

orbit is

r_{n} = n^{2} r_{1}

.
The second excited state is

n = 3

(ground

n = 1

, first excited

n = 2

, second excited

n = 3

r_{3} = 3^{2} \times 5.3 \times 1 0^{- 11} = 9 \times 5.3 \times 1 0^{- 11} = 4.77 \times 1 0^{- 10} m .

r_{3} = 4.77 \times 1 0^{- 10} m

CBSE Class 12 Board · 2010 · Subjective