Question

Consider the following energy levels of a hypothetical atom:
E₄ −1.51 × 10⁻¹⁹ J

E₃ −5.11 × 10⁻¹⁹ J

E₂ −1.15 × 10⁻¹⁸ J

E₁ −1.85 × 10⁻¹⁸ J

(a) What is the wavelength of the photon needed to excite an electron from E₁ to E₄? (in m)

(b) What is the energy (in joules) a photon must have in order to excite an electron from E₂ to E₃?

(c) When an electron drops from the E₃ level to the E₁ level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process.

Answer 1

a)

dE = Efinal - Einitial = (1.51*10^-19)-(1.85*10^-18) = 1.699*10^-18 J

WL = h c / E

h = Planck Constant = 6.626*10^-34 J s

c = speed of particle (i.e. light) = 3*10^8 m/s

E = energy per particle J/photon

WL = wavelength in meters

WL = (6.626*10^-34)(3*10^8)/(1.699*10^-18)

WL = 1.169*10^-7 m

b)

Energy required

E = E3-E2 = (5.11*10^-19)-(1.15*10^-18) = 6.39*10^-19 J required to absorb

c)

dE = E1-E3 = (1.85*10^-18)-(5.11*10^-19) =1.339*10^-18 J

WL = (6.626*10^-34)(3*10^8)/(1.339*10^-18

WL = 1.4845*10^-7 m