Question 6 of 8beginner🔧 ApplyNumerical2 marks

The radius of the innermost electron orbit of a hydrogen atom is 5.3×105.3 \times 10⁻¹¹ m. What are the radii of the n = 2 and n = 3 orbits?

Correct Answer

The radius of the n = 2 orbit is 2.12×102.12 \times 10⁻¹⁰ m and the radius of the n = 3 orbit is 4.77×104.77 \times 10⁻¹⁰ m.

Exercise: EXERCISES | Q: 12.7 | (Page 16)
For More Understanding

Explanation

According to Bohr's model, the radius of the nth orbit is given by r_n = (n²/m)(h/2π)²(4πε₀/e²). This shows that the radius is proportional to n². Since the innermost orbit corresponds to n = 1 with radius r₁ = 5.3×105.3 \times 10⁻¹¹ m, we can use the relation r_n = n² × r₁ to find the radii of higher orbits.

Solution Steps

  1. Step 1: From Bohr's model, the radius of nth orbit is r_n ∝ n². The formula r_n = (n²/m)(h/2π)²(4πε₀/e²) shows that radius is proportional to n².

  2. Step 2: Given radius of innermost orbit (n=1): r₁ = 5.3×105.3 \times 10⁻¹¹ m

  3. Step 3: For n = 2: r₂ = (2)² × r₁ = 4×5.34 \times 5.3 × 10⁻¹¹ = 2.12×102.12 \times 10⁻¹⁰ m

  4. Step 4: For n = 3: r₃ = (3)² × r₁ = 9×5.39 \times 5.3 × 10⁻¹¹ = 4.77×104.77 \times 10⁻¹⁰ m

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