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

ID: 1518654 • Letter: 1

Question

1) Find the energy of the ground state (n = 1) of a proton in a one-dimensional box of length 1.6 nm. Answer in units of meV.

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.

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.

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.

1) E = (n²²²)/(2ma²)
n=1, h is planck's constant,h=6.626x10-34 j

m is mass of particle (mass of proton),i.e m=1.672x10-27 kg

a is length of box a = 1.6 nm.

E=[2 x(6.626x10-34 )2 ]/(2x1.672x10-27x(1.6x10-9 m)2 )

=5.056x10-22 j

2)here E=(n'²-n²)(²²)/(2ma²)

where n' is initial, and n is final n' =2,n=1

=(4-1)( ²²)/(2ma²)

= 3x(2 x(6.626x10-34 )2 ]/(2x1.672x10-27x(1.6x10-9 m)2 )

=1.518x10-21

E = hf = hc/

=hc/E

=(6.626x10-34 x3x108 )/(1.518x10-21 )

=1.30948x10-4 m

=130.9x10-6 =130.9m

3)E=(n'²-n²)(²²)/(2ma²) n' 3,n=2

=5x(2 x(6.626x10-34 )2 ]/(2x1.672x10-27x(1.6x10-9 m)2 )

=2.528x10-21

=hc/E

=(6.626x10-34 x3x108 )/( 2.528x10-21 )

=78.6x10-6

=78.6 m

4) E=(n'²-n²)(²²)/(2ma²) n' 3,n=1

=8x( 2 x(6.626x10-34 )2 ]/(2x1.672x10-27x(1.6x10-9 m)2 )

=4.045x10-21

=hc/E

=(6.626x10-34 x3x108 )/( 4.045x10-21 )

=49.08x10-6

=49.08 m

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