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

Question

Part 1: Find the energy of the ground state (n = 1) of a proton in a one-dimensional box of length 2.6 nm. Answer in units of meV.

Part 2: Calculate the wavelength of electromagnetic radiation emitted when the photon makes a transitionfromn=2 to n=1.

Answer in units of m.

Part 3: Calculate the wavelength of electromagnetic radiation emitted when the photon makes a transitionfromn=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)
Energy is given by,
E = (h^2*^2)/(2*m*L^2)
E = ((1.054*10^-34)^2 * ^2)/(2*1.67 * 10^-27 * (2.6*10^-9)^2 )
E = 4.856 * 10^-24 J
E = 0.03035 meV

(2)
1/ = 1.097 * 10^7 ( 1/nf^2 - 1/ni^2)
1/ =  1.097 * 10^7 ( 1/1^2 - 1/2^2)
= 121.5 nm

(3)
1/ =  1.097 * 10^7 ( 1/2^2 - 1/3^2)
= 656.3 nm

(4)
1/ =  1.097 * 10^7 ( 1/1^2 - 1/3^2)
= 102.5 nm

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