A-level Physics (Advancing Physics)/Energy Levels/Worked Solutions

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The following table gives the wavelengths of light given off when electrons change between the energy levels in hydrogen as described in the first row:

Transition of n 3→2 4→2 5→2 6→2 7→2 8→2 9→2 ∞→2
Wavelength (nm) 656.3 486.1 434.1 410.2 397.0 388.9 383.5 364.6
Colour Red Blue-green Violet Violet (Ultraviolet) (Ultraviolet) (Ultraviolet) (Ultraviolet)

1. Calculate the potential energy of an electron at level n=2.

2. Calculate the difference in potential energy between levels n=2 and n=3.

This time, let's derive a general formula:

3. What is the potential energy of an electron at level n=3?

4. If an electron were to jump from n=7 to n=5, what would the wavelength of the photon given off be?

5. Prove that the wavelength of light emitted from the transition n=4 to n=2 is 486.1 nm (HINT: and )