Potential/Kinetic/Total Energy of hydrogen atom absorbing photon

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SUMMARY

A hydrogen atom in the n = 2 state absorbs a photon with a wavelength of 380 nm, resulting in a total energy change of 5.23×10-19 J. The potential energy (U) and kinetic energy (K) formulas are essential for further calculations, where U = E - K. The discussion highlights that the kinetic energy of the electron decreases as it moves away from the nucleus, while the potential energy increases due to the nature of the Coulomb force and energy conservation principles. The Virial Theorem is suggested as a potential resource for deeper understanding.

PREREQUISITES
  • Understanding of quantum states, specifically hydrogen atom energy levels
  • Familiarity with the concepts of kinetic energy (KE) and potential energy (U)
  • Knowledge of the Coulomb force and its implications in atomic physics
  • Basic grasp of the Virial Theorem in physics
NEXT STEPS
  • Study the derivation of kinetic energy in atomic systems using KE = 1/2 mv2
  • Explore the relationship between potential energy and distance in electrostatic interactions
  • Investigate the application of the Virial Theorem in quantum mechanics
  • Learn about energy transitions in hydrogen atoms and their spectral implications
USEFUL FOR

Students studying quantum mechanics, physicists interested in atomic energy levels, and educators teaching concepts of energy in atomic systems.

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Homework Statement



A hydrogen atom in the n = 2 state absorbs a photon with wavelength 380 nm.


Q1. Find the change in the atom’s total energy.
Q2. Find the change in the atom’s potential energy
Q3. Find the change in the orbiting electron’s kinetic energy.

Homework Equations



E=E0/n2


The Attempt at a Solution



Q1 I solved correctly so I know total E = 5.23×10−19 J
Q2 I know U = E - K, but I don't know the formulas for K or for U so I'm stuck here for Q2 and Q3.

Direction please? Also, I'm having difficulty in understanding why the kinetic energy of the electron decreases as you move away from the nucleus, and why the potential energy increases. Thanks.
 
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Why the kinetic energy of the electron decreases:
KE = 1/2 mv^2
a = v^2/r, so v = (ar)^1/2, so:
KE = 1/2 mar, where a is given by:
F = ma = KQq/r^2 so a = KQq/(mr^2) so:
KE = 1/2 Kqq/r

Why the potential energy increases:
At r = infinity, the proton and electron would feel no attraction. Bump them a little closer than infinity, and they feel the Coulomb force, which means they experience an acceleration. If they accelerate, their kinetic energy increases. To conserve energy, we conclude that since kinetic energy increases, potential energy decreases as the distance decreases.

I'm not sure if your text covers it, but if it does, try the Virial Theorem.
 

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