# Potential/Kinetic/Total Energy of hydrogen atom absorbing photon

• louza8
In summary, the conversation discusses a hydrogen atom in the n = 2 state that absorbs a photon with wavelength 380 nm. The change in the atom's total energy is given as 5.23×10−19 J. However, the formulas for the change in potential and kinetic energy are unknown, leading to difficulties in solving for them. The decrease in kinetic energy as the electron moves away from the nucleus is due to a decrease in acceleration, while the increase in potential energy is a result of the Coulomb force between the proton and electron. The Virial Theorem may provide further insight into the relationship between potential and kinetic energy.
louza8

## 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.

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.

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.

## 1. What is the difference between potential, kinetic, and total energy in a hydrogen atom?

Potential energy refers to the energy an atom has due to its position or arrangement of electrons. Kinetic energy is the energy an atom has due to its motion. Total energy is the sum of potential and kinetic energy.

## 2. How does a hydrogen atom absorb a photon and change its energy state?

When a photon of the correct energy is absorbed by a hydrogen atom, it causes the electron to jump to a higher energy level or orbit. This increases the potential energy of the atom.

## 3. What is the equation for calculating the potential energy of a hydrogen atom?

The potential energy of a hydrogen atom can be calculated using the equation: E = -13.6/n2 eV, where n is the principal quantum number representing the energy level of the atom.

## 4. How does the total energy of a hydrogen atom change when it absorbs a photon?

The total energy of a hydrogen atom increases when it absorbs a photon. This is because the potential energy increases due to the electron jumping to a higher energy level, while the kinetic energy remains constant.

## 5. Can a hydrogen atom emit a photon and release energy?

Yes, a hydrogen atom can emit a photon and release energy when an electron falls from a higher energy level to a lower one. This results in a decrease in potential energy and an increase in kinetic energy of the atom.

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