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MHT CET · Physics · Atomic Physics

When a hydrogen atom is raised from the ground state to the excited state

  1. A potential energy increases and K.E. decreases.
  2. B potential energy decreases and K.E. increases.
  3. C both K.E. and potential energy will increase.
  4. D both K.E. and potential energy decreases.
Verified Solution

Answer & Solution

Correct Answer

(A) potential energy increases and K.E. decreases.

Step-by-step Solution

Detailed explanation

K.E. \(\propto \frac{1}{r}\)
That is kinetic energy is inversely proportional to the radius of orbit. If \(r\) increases then K.E. decreases. Hence we can conclude that when an electron is excited to a higher energy level its kinetic energy decreases.
Similarly formula for potential energy for the hydrogen atom can be given as
\(\text {P.E. }=-\frac{k Z e^2}{r}\)
Where \(k\) is constant, \(e\) is charge on an electron, \(r\) is radius of orbital and \(Z\) is the number of protons in the nucleus. We can see that potential energy is also inversely proportional to the radius of orbital and we can write it as
P. E. \(\propto-\frac{1}{r}\)
Although it is inversely proportional but due to negative sign, when the radius is increased, the potential energy is also increased.
Hence, when a hydrogen atom is raised from ground state to excited state, its potential energy increases