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Chapter 34: Problem 58

A hydrogen atom is in its ground state when its electron absorbs a 48 -eV photon. What's the energy of the resulting free electron?

Short Answer

Expert verified
The energy of the resulting free electron is 34.4 eV.

Step by step solution

01

Identify the initial energy state of the electron in the hydrogen atom

In a hydrogen atom, when the electron is in its ground state (n=1), the energy level is -13.6 eV. This is the initial energy of the electron.
02

Calculate the total energy absorbed by the electron

The electron in the ground state absorbs a photon with an energy of 48 eV. So, the total energy absorbed by the electron would be the energy of the absorbed photon added to the energy of the electron in its initial state. Therefore, the total energy absorbed is -13.6 eV (initial energy) + 48 eV (energy of photon) = 34.4 eV.
03

Determine the energy of the resulting free electron

According to the energy conservation principle, the energy absorbed by the electron becomes the energy of the resulting free electron. Thus, the energy of the resulting free electron is 34.4 eV.

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