Energy diagram for an atom contains an excited electron at n = 4 level (see below...

Energy diagram for an atom contains an excited electron at n = 4 level (see below table). Calculate the longest wavelength of light that is emitted.

Answer must be in meters!

Energy Level (n)	Energy
n=1	1.13 x 10^-27 J
n=2	2.05 x 10^-27 J
n=3	2.40 x 10^-27 J
n=4	2.99 x 10^-27 J
n=5	3.97 x 10^-26 J

Please thoroughly explain every step and equation as I've been attempting this question for hours and still do not understand.

Solutions

Expert Solution

This question is easier in a numerical manner and difficult in a theoretical manner therefore I shall first explain the the theoretical part which will help you to conclude what you have to solve numerically.

The questions says that energy is emitted which means that the electron has already observed energy and is already sitting at an excited state and now we have left it so that it can move freely towards any lower shell in order to attain lower energy.

When the energy change is maximum it means that the the lowest wavelength energy has been admitted as we know that the formula for energy is E =hc/wavelength.

So lower the the energy higher is the value of the wavelength taking part in the transition.

As we know the excited state of the electron is at n is equal to 4, so in order to EMIT energy it will move towards 3 or 2 or 1 shell.

Now if we calculate the change in energy for each of the transition, the highest amount of energy change will give the lowest wavelength value and the lowest energy change will give the highest wavelength value.

now if we start calculating it is quite visible that when the electron moves from the fourth shell to the first shell it emits the highest amount of energy and therefore the wavelength will be the lowest on the other hand when the electron moves from the fourth shell to the third shell the the lowest amount of energy is liberated and therefore being inversely proportional to wavelength, the value of wavelength increases on this transition.

So we will find the energy for the transition from 4th to third shell and use the formula of energy to find the wavelength related to this transition.

I hope you understand the numerical and kindly provide us with your feedback.

queen_honey_blossom answered 1 year ago

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