Question

The radius of innermost electron orbit of a hydrogen atom is 5.3 × 10-11 m. What is the radius of orbit in the second excited state?​

Answer 1

Answer:

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:

r₂ = (n)²r₁

= 4 x 5.3 x 10⁻¹¹ = 2.12 x 10⁻¹⁰ m

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

r₃ = (n)² r₁

= 9 x 5.3 x 10⁻¹¹ = 4.77 x 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.

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Answer 2

Answer:

The radius of the innermost orbit of a hydrogen atom,

$r2 = 5.3 × {10}^{ - 11} \: m.$

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

$r2 = (n) {}^{2} r1$

$= 4 \times 5.3 \times 10 {}^{ - 11} = 2.12 x 10 {}^{ - 11} \: m$

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

$r3 = (n) {}^{2} r1$

$= 9 \times 5.3 \times 10 {}^{ - 11} = 4.77 \times 10 {}^{ - 11} \: m$

• 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.