Question

An electron is in the ground state of an infinite square well. The energy of the ground state is E1 = 1.13 eV.

(a) What wavelength of electromagnetic radiation would be needed to excite the electron to the n = 7 state? nm

(b) What is the width of the square well? nm

Answer 1

A)

R = Rydberg constant =10 973 731.6 m^-1

1/λ = R* ( 1/n²₁ - 1/n²₂ )

from above equation  

λ≈9.30252×10^-8   = 93.0252  nm   answer 

B)

energy in any nth state is given by

E1 = 1.13 eV = 1.13*1.6*10^-19 J

En = n²h² / 8mL²

E₁ = 1² *( 6.626*10^-34)^2 / ( 8*9.11*10^-31*L^2)

1.13*1.6*10^-19 = 1² *( 6.626*10^-34)^2 / ( 8*9.11*10^-31*L^2)

from bove eqution   width of the square well = L

L = 5.77229×10^-10  = 0.577229  nm   answer 

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