Part 1: Find the energy of the ground state (n = 1) of a proton in a one-dimensi
ID: 1520967 • 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.
Explanation / Answer
(1)
E= n^2 h^2/ 8 mL^2
=1^2 ( 6.63 * 10^-34)^2/ 8 ( 1.6 * 10^-27) ( 1.1* 10^-9)^2
=2.83 * 10^-23 J ( 1 eV/ 1.6 * 10^-19)
=0.177m eV
E2 = n^2 E1= 2^2 ( 0.177 meV) =0.708 meV
E3 = n^2 E1 = 3^2 ( 0.177 meV) =1.59 meV
(2)
lamda = hc/ E2- E1 = 1240 eV nm/0.708-0.177) meV = 2335m
(3)
lamda = hc/ E3- E2 = 1240 eV nm/1.59-0.708) meV = 1405m
(4)lamda = hc/ E3- E2 = 1240 eV nm/1.59-0.177) meV = 877.56m