Question

In the spectrum of the atom, two yellow lines are emitted, one at 5890Å and the other at 5896Å
A. Which of the two lines has a higher energy for the photon?
B. Calculate the energy difference between two photons at the wavelengths mentioned

Answer 1

(A.) Energy of photon is inversely proportional to wavelength. Lower the wavelength, higher will be the energy. Hence photon with wavelength = 5890 A^o has higher energy.

(B.) Energy of photon = [(h) * (c)] / (wavelength)

where h = Planck's constant = 6.626 x 10^-34 J.s

c = speed of light = 3.0 x 10⁸ m/s

when wavelength = 5890 A^o = 5890 x 10^-10 m

E₁ = [(6.626 x 10^-34 J.s) * (3.0 x 10⁸ m/s)] / (5890 x 10^-10 m)

E₁ = 3.375 x 10^-19 J

when wavelength = 5896 A^o = 5896 x 10^-10 m

E₂ = [(6.626 x 10^-34 J.s) * (3.0 x 10⁸ m/s)] / (5896 x 10^-10 m)

E₂ = 3.371 x 10^-19 J

Difference in energy = (E₁) - (E₂)

Difference in energy = (3.375 x 10^-19 J) - (3.371 x 10^-19 J)

Difference in energy = 3.43 x 10^-22 J