In an alternate universe, electron energies in an atom are found to obey the
following equation where n is the principle quantum number:
E = 3.0 x 10^(-19) J * nm * (1/n^2)
..where n is the principle quantum number
A gas discharge lamp, like the lamps used in lab, contains only atoms
from the alternate universe. You turn the lamp on and observe the
spectrum. Two energy transitions that occur within the visible spectrum
(400-700 nm), provide the wavelength of the photon and corresponding
energy levels that produce the photon.
...Where do I even begin?
To determine the energy levels and the corresponding wavelengths of the photons emitted by the gas discharge lamp, you need to find the values of the principle quantum number (n) that satisfy the given condition for the visible spectrum (400-700 nm).
Here's how you can begin:
1. Start by finding the energy range within the visible spectrum. The visible spectrum ranges from 400 nm (violet) to 700 nm (red).
2. Use the energy equation you provided to find the energy values for different values of n. Plug in the values of n and calculate the energy for each level.
E = 3.0 x 10^(-19) J * nm * (1/n^2)
Substitute the energy range (in nm) and solve the equation for different values of n within that energy range.
3. Look for the energy levels (n values) that produce energy values within the visible spectrum. These will be the energy levels responsible for the emission of photons in the visible range.
4. Once you have determined the energy levels (n values), you can find the corresponding wavelengths (in nm) of the emitted photons using the equation:
λ = c / E
where λ is the wavelength, c is the speed of light (approximately 3 x 10^8 m/s), and E is the energy of the transition (from the previous calculation).
5. Calculate the corresponding wavelength for each energy level (n) within the visible spectrum to determine the wavelengths of the photons emitted.
By following these steps, you can find the energy levels and corresponding wavelengths of the photons emitted by the gas discharge lamp within the visible spectrum.