How Do You Calculate the Minimum Wavelength to Ionize Hydrogen Atoms?

[xregina12]

Hi, below is a question from my first quantum mechanics homework. I haven't taken quantum mechanics before and I don't how to approach the question exactly. For part a, I believe I can use the equation Emax=1/2mv^2=hv-hvo. vo=binding energy. For the minum wavelength of light, do I assume the electrons emitted have no velocity after emission and set hv-hvo=0? Can someone please guide me with this problem or give me some suggestions? I would really really appreciate this!

7. Quantum mechanics predicts that the binding energy of the ground state of the H atom is -
13.6 eV. Insight into the magnitude of this quantity is gained by considering several methods by
which it can be measured.
a) Calculate the minimum wavelength of light that will ionize H atoms in their ground state.
b) Assume the H atom is ionized by collision with an electron that transfers all its kinetic energy
to the H atom in the ionization process. Calculate the speed of the electron before the collision.
Express your answer in m s-1 and in miles hour--1.

 

[Claude Bile]

Firstly, I believe part a) should read maximum wavelength, not minimum.

For part a), firstly work out what the minimum photon energy needs to be to ionise the H atom, then use E = hc/lambda to determine the corresponding wavelength.

For part b), determine the kinetic energy of the incident electron then work out the velocity using KE = 1/2 mv^2.

Claude.