Question

Some atomic processes can result in the emission of an electron from the atom. Electrons emitted in this way can have discrete values of kinetic energy, which depend on the atomic energy levels. The probability that the electron has a particular value depends on interacions within the atom.

Suppose a particular atomic process results in three values of the electron kinetic energy:

• Ψ₁ has E_e = 10 eV, with probability 0.2.
• Ψ₂ has E_e = 16 eV, with probability 0.3.
• Ψ₃ has E_e = 34 eV, with probability 0.5.

The electron's wave function can be written as a quantum superposition: Ψ = aΨ₁ + bΨ₂ + cΨ₃

What are the magnitudes of a, b, and c?

1) |a| =

2) |b| =

3) |c| =

4) Suppose we measure the energies of a large number of electrons that are all described by the wave function, Ψ, that you have just calculated. What will be the average value of your energy measurements? E_av =

5) Suppose we measure the kinetic energy of an outgoing electron and obtain KE = 16 eV. If we then measure the wavelength. What result will we obtain? λ =

Answer 1