Part 1: Find the energy of the ground state (n = 1) of a proton in a one-dimensi

ID: 1521365 • Letter: P

Question

Part 1: Find the energy of the ground state (n = 1) of a proton in a one-dimensional box of length 1.1 nm. Answer in units of meV.

Part 2: Calculate the wavelength of electromagnetic radiation emitted when the photon makes a transition from n = 2 to n = 1. Answer in units of m.

Part 3: Calculate the wavelength of electromagnetic radiation emitted when the photon makes a transition from n=3 to n=2. Answer in units of m.

Part 4: Calculate the wavelength of electromagnetic radiation emitted when the photon makes a transition from n=3 to n=1. Answer in units of m.

Here, En = (n2h2)/(8mL2)

Part 1) energy of the ground state = (6.63 * 10-34)2/(8 * 1.67 * 10-27 * 1.1 * 1.1 * 10-18)

= 2.719 * 10-23 J

= 0.1699 meV

Part 2) Here, energy difference = 13.6 * (3/4) * 1.6 * 10-19

= 1.632 * 10-18 J

=> wavelength = (6.63 * 10-34 * 3 * 108)/(1.632 * 10-18)

= 0.1218 m

Part 3) wavelength = (6.63 * 10-34 * 3 * 108)/(3.022 * 10-19)

= 0.6581 m

Part 4) wavelength = (6.63 * 10-34 * 3 * 108)/(1.934 * 10-18)

= 0.1028 m