HW Question 1.57

[Danielle Sumilang - 1F]

Hello!

I am having a little trouble figuring out this question. It states that lines in the Balmer series of the hydrogen spectrum are observed at 656.3, 486.1, 434.0, 410.2 nm and asks to find the wavelength of the next line in the series. How would I begin the problem?

[Susu Le 1F]

Since the question states that it’s the Balmer series, the electron is dropping from a higher energy level to the energy level of n=2. The greater the wavelength, the smaller the energy, so:

656.3 nm corresponds the the smallest transition, which is from n=3 to n=2.
486.1 nm corresponds to n=4 to n=2.
434.0 nm —> n=5 to n=2
410.2 nm —> n=6 to n=2

The next line in the series should show the light emitted when the electron transitions from n=7 to n=2.
Use the equation En=-hR/n^2 to find the energy of the electron at n=7 and n=2. Then, subtract E7-E2, and this is the energy of the light emitted. Then use E=hv to find the frequency of the light, and then find the wavelength of this light.

[Danielle Sumilang - 1F]

Thank you so much! That was really helpful. Should the wavelength always be given in nm or would it be ok to just leave the answer in meters?

[Amanda 1A]

The question usually specifies if it wants it in nm. If it doesn't, I'm sure both answers will get full credit.