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Q. 40

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

The ionization energy of an atom is known to be . The emission spectrum of this atom contains only the four wavelengths and . Draw an energy-level diagram with the fewest possible energy levels that agrees with these experimental data. Label each level with an appropriate quantum number. Hint: Don’t forget about the selection rule.

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Step by Step Solution

Wavelength of photon emitted:

The allowed transitions are determined form the following usual selection rules

If the above selection rules are not satisfied, no other transitions are allowed between the energy levels.

The wavelength of photon emitted as,

Rearranging the above equation for the energy difference,

.....(1)

Here, is planck's constant and is speed of light in vacuum .

Conversion of unit wavelength:

Convert the unit of wavelength from to .

Substitute for for and for in the above equation.

Conversion of unit wavelength:

Convert the unit of wavelength from to .

Substitute for for and for in the above equation.

Conversion of unit wavelength:

Convert the unit of wavelength from to .

Substitute for for and for in the above equation.

Conversion of unit wavelength:

Convert the unit of wavelength from to .

Substitute for for and for in the above equation.

Definition with graph explanation:

For the wavelength , the difference in energy levels is so we can think of it as the maximum transition. So if we take the ground state as . The one state will be of .

There is possibility of another state having energy .If we take the energy level as .

Then we can get the exact energy levels corresponding to given data as

So we can level the following energy levels:

Labeling each energy:

Let us label each energy level with appropriate . For this we need to consider .

Let state is of l.e., State can be i.e. . Then state should also be of i.e., .

Diagram:

So we can have the following diagram:

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