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Difficulty: EasyAtomic Models

According to Bohr's atomic model of the hydrogen atom, what condition must be satisfied by an electron moving in a stable stationary orbit?

  1. Its orbital angular momentum is an integral multiple of h2π\frac{h}{2\pi}.Answer
  2. B
    Its total energy is proportional to light intensity.
  3. C
    Its orbital frequency increases continuously as it radiates energy in the orbit.
  4. D
    Its total mechanical energy is zero in all allowed stationary orbits.

Answer

An electron moves in a stable stationary orbit when its orbital angular momentum is an integral multiple of h2π\frac{h}{2\pi}.
Bohr's fundamental postulate states that an electron can revolve around the nucleus only in certain non-radiating orbits (stationary states) where its orbital angular momentum is an integral multiple of h2π\frac{h}{2\pi}.

Step-by-Step Solution

1
Recall Bohr's postulates for the hydrogen atom
Identify that stable orbits require quantization of orbital angular momentum.
Bohr introduced quantization to explain why orbiting electrons do not continuously emit radiation and collapse into the nucleus.
2
State the mathematical formula for angular momentum quantization
L=mvr=nh2πL = mvr = \frac{nh}{2\pi}, where nn is an integer (1,2,3,…1, 2, 3, \dots) and hh is Planck's constant.
Only specific discreet orbits meeting this condition are allowed stationary states.

Key Concept

Quantization of Angular Momentum in Bohr's Model
Estimated Time:45s
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Topics

Atomic Models

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