Question 5 of 8intermediate🔧 ApplyNumerical5 marks

(a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the n = 1, 2, and 3 levels. (b) Calculate the orbital period in each of these levels.

(a)
Answer

Speed of electron: n = 1: 2.18×102.18 \times 10⁶ m/s, n = 2: 1.09×101.09 \times 10⁶ m/s, n = 3: 0.727×100.727 \times 10⁶ m/s

(b)
Answer

Orbital period: n = 1: 1.53×101.53 \times 10⁻¹⁶ s, n = 2: 1.22×101.22 \times 10⁻¹⁵ s, n = 3: 4.13×104.13 \times 10⁻¹⁵ s

Explanation

This question applies Bohr's model quantization conditions. The speed formula v_n = v₁/n comes from combining angular momentum quantization (mvr = nh/2π) with Coulomb force equilibrium. The orbital period uses the relation T = 2πr/v with r_n = n²a₀.

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