What is the shortest wavelength photon emitted in a hydrogen atom?

[Kennedy111]

Homework Statement

Calculate the shortest wavelength photon that is emitted in the hydrogen atom.

Energy when n = 1 = -13.6 eV

Homework Equations

E = hc/λ
λ = hc/E

The Attempt at a Solution

Well as far as I understand, when the electron is in the n = 1 energy level it has it's lowest energy, which is -13.6 eV. I believe this is where the shortest wavelength will be...
λ = hc/E
= (4.14 x 10^-15 eV*s)(3.00 x 10^8 m/s) / -13.6 eV
= approx 9.13 x 10^-8 m

Was my method correct? I would really just like a second opinion. Thank you!

 

[ehild]

The method is correct, but the photon energy is positive: 13.6 eV, the same the electron loses when it becomes bounded to the hydrogen atom. You divided by -13.6 eV, then ignored the sign, which is wrong.

ehild

 

[apelling]

Are n't photons produced when an electron jumps between energy levels not stay on one level? The shortest wavelength photon will be the one with least energy produced by an electron transition of the smallest energy. If the electron is to end up at n=1, the shortest wavelength photon comes from a jump from n=2 to n=1 (-3.4eV to -13.6eV).

 

[ehild]

An electron can jump from any level to a deeper one, even from n=infinite (free electron) can get bounded to the atom by jumping onto the first level. See:http://en.wikipedia.org/wiki/Hydrogen_spectral_series

ehild

 

[apelling]

Sorry I have just realized my mistake. Shortest wavelength comes from the largest energy not the smallest.