Chapter 39 Problem 2 An electron trapped in a onedimensional

Chapter 39, Problem 2

An electron, trapped in a one-dimensional infinite potential well 268 pm wide, is in its ground state. How much energy (in eV) must it absorb if it is to jump up to the state with n = 6?

Solution

Width L = 268 pm= 268 x10 ^-12 m

Energy of electron in n=6 state is E = n² h ²/ (8mL ²)

Where n = 6

           h = Planck\'s constant = 6.625 x10 ^-34 J s

           m = mass of electron = 9.1 x10 ^-31 kg

Substitute values you get E = [36 x(6.625 x10 ^-34 ) ² ] /[8 x9.1 x10 ^-31 x (268x10 ^-12 ) ² ]

                                          = 3.021 x10 ^-17 J

                                           = [(3.021x10 ^-17 )/(1.6x10 ^-19) ]eV

                                           = 188.8 eV

Energy of electron in ground state is E \' = n² h ²/ (8mL ²)

Where n = 1

           h = Planck\'s constant = 6.625 x10 ^-34 J s

           m = mass of electron = 9.1 x10 ^-31 kg

Substitute values you get E = [1 x(6.625 x10 ^-34 ) ² ] /[8 x9.1 x10 ^-31 x (268x10 ^-12 ) ² ]

                                          = 8.391 x10 ^-19 J

                                           = [(8.391x10 ^-19 )/(1.6x10 ^-19) ]eV

                                           = 5.244 eV

Required energy = E - E \'

                         = 183.55 eV