How much energy does the electron have initially inthe n=4 excited state?

energy-electron

#1

How much energy does the electron have initially inthe n=4 excited state?
Enter your answer numerically in joules.
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The second question is what I need help with:
What is the change in energy if the electron from Part A now dropsto the ground state?
Enter your answer numerically in joules.

Answer:

The expression for the energy of an electron in an excited state is given below:
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The electron when it is initially in the (n = 4) excited state is image
The energy of the electron in the excited state (n = 4) is obtained by substituting the values in the equation. The unit of energy is in joules.

Initially, find the wavelength of light emitted by the electron using Rydberg’s formula.
The Rydberg equation is given below:
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The wavelength is calculated below:
image
Finally, calculate the change in the energy of the electron when it drops to ground state, using plank’s equation.
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The change in energy, if the electron from excited state (n = 4) drops to the ground state, is image

The electron drops from an excited energy state to a ground state by releasing energy in the form of light. The light has particular wavelength which is calculated using Rydberg’s equation. The frequency of light is calculated from the speed of light and the wavelength of light. Finally, the energy of the electron can be calculated using plank’s equation.