Using the Bohr model, calculate the radius for the electron in the n=1 energy level for a hydrogen atom (1 proton and 1 electron) and a helium cation (2 protons, 2 neutrons and 1 electron). Explain why the radii are either the same or different.

Physical chemistry foe biochemistry II

1. (25 pts) Using the Bohr model, calculate the radius for the electron in the n=1 energy level for a hydrogen atom (1 proton and 1 electron) and a helium cation (2 protons, 2 neutrons and 1 electron). Explain why the radii are either the same or different.
2. (20 pts) Explain the difference between an eigenvalue and an expectation value (<3-5 sentences).
3. (25 pts) What is the kinetic energy for a proton with the following wavefunction? (Hint: the ‘m-1’ in the wavefunction is the unit of ‘meter’ to the power of -1)

4. (20 pts) Calculate the expectation value for the ‘F’ operator given the following wavefunction and relationships.
5. (10 pts) The particle in a 1D box has an infinite potential, V = ∞, at x < 0 and x > L. A modified particle in a 1D box additionally has an infinite potential at exactly x = L / 2. Using equations, show how this modifies the eigenfunctions and energy levels.

|Ψ(x)⟩ = 1

3 cos(3m −1 x)

|ψ⟩ = c|φ1⟩ + 2c|φ2 ⟩

̂

F|φ1⟩ = 1 ⋅ |φ2⟩

̂

F|φ2⟩ = 0

c* = c

⟨φi | φj ⟩ = 0 when i ≠ j

⟨φi | φj ⟩ = 1 when i = j