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CGP EDU Academic Team
Published on: August 13, 2026
Consider Bohr's theory for hydrogen atom. The magnitude of angular momentum, orbit radius and velocity of the electron in n th energy state in a hydrogen atom are λ , r & v respectively. Find out the value of ' x' , if product of v, r and λ (vr λ ) is directly proportional to n x .
Text Solution
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Angular momentum, λ = mvr = 
∴ λ ∝ n
Radius, r = 0.529 
Å r ∝ n 2 For same Z
Velocity, v = 2.18 × 10 6 
m/s ∴ v ∝ 
∴ v r λ ∝ n × n 2 × 
But, v r λ ∝ n x (given)
∴ n 2 = n x
∴ x = 2
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