Sapling HW Spectral Lines/Energy Levels

[Jolie Sukonik 2B]

The electron in a hydrogen atom is excited to the n=7 shell and emits electromagnetic radiation when returning to lower energy levels. Determine the number of spectral lines that could appear when this electron returns to the lower energy levels, as well as the wavelength range in nanometers.

I know the amount of spectral lines that could appear = 6. Therefore, the highest energy would be emitted when n= 7 --> n=1, and the lowest when n=7 --> n=6. However, I'm really struggling with finding the range of wavelengths in nanometers. Can someone walk me through this?

[Chanel Mao 3D]

Hi!

Since you know that n=7 -> n=1 has the highest energy emitted, you would need to find the change in energy with the Rydberg Equation (which should be on the equation sheet). After that, you would use the equation lamda=(h*c)/E to get the wavelength in meters. You would then need to multiply this number by 10^9 to get the length in nanometers. To get the range in wavelengths, you would do the same thing for n=7 -> n=6. Hope this helps!

[Hailey Qasawadish 2J]

You basically would have to find the energy difference twice. Once from n=1 to n=7, and then again from n=6 to n=7. I used Rydberg's equation, found the frequency, then used E=hv to find the energy. I did this for each jump. The values you get for your energy are the endpoints for your range. Hope this helps!

[Giselle Granda 3F]

So for this problem once you know the energy levels for the highest and lowest energies, you would use the equation En=-hR/n^2 to solve for the energy at the n2=7 level and n1=6 level. Then you use the equation deltaE=E1-E2 to find the change in energy for the electron. You can then solve for the wavelength using the equation lambda=hc/E (but remember to change the sign of the energy you solved for in the previous step from negative to positive). That will you your first wavelength for the range. To find the wavelength for the electron when going from the n2=7 level to the n1=1 level, you follow the same process. First solve for E of both levels, then solve for the change in E, then solve for wavelength using the change in E. I hope this is not too confusing!

[Jack_Pearce_2H]

Hi!

What I did as use the Bohr Frequency equations [v=Rh((1/n2^2)-(1/n1^2))] to solve for v then use E=hv to solve for the energy. Make sure to pay attention to the values so they make sense logically! Hope this helps :)