The energies in a 2D particle-in-a-box are given by h² Exm, 3m² = (1, ²+1, ²) 2+ n ,n 8mL2 in which the box is a square enclosure with Lx = Ly = L, and nx, ny = 1, 2, 3,.... (a) If the particle is an electron and L = 300 pm (assume three significant figures), find the value of the lowest energy level in units of 10-18 J (that is, if the energy is 5.00 × 10-18 J, you would report it as "5.00").

The lifetimes of the levels in a hydrogen atom are of the order of 10-8 s. Find the energy uncertainty of the first excited state and compare it with the energy of the state. 3 p RO

Problem 9: Rutherford Scattering A gold foil (5.9×1022 atoms/cm³) of "hair" thickness 80 µm is used in a Rutherford experiment to scatter a particles with energy 5 MeV. Find the fraction of particles scattered at angles 0 > 30°.

Electrons are fired at a rectangular potential energy barrier, once every 149 ms. If the barrier is 2.55 nm thick and has a height that exceeds the energy of the incident electrons by exactly 712 meV, how long on average would you expect to wait for one electron to pass through the barrier?