Question

In an atom X, electrons absorb the energy from an external source. This energy “excites” the electrons from a lower-energy level to a higher-energy level around the nucleus of the atom. When electrons return to the ground state, they emit photons.

The figure below is the energy level diagram of atom X with three energy levels, E₁ = 0.00eV, E₂ = 1.78eV and E₃ = 2.95eV. The ground state is considered 0 eV for reference. The transition of electrons takes place between levels E₁ and E₂.

1. What wavelength of radiation is needed to excite the atom to energy level E₂ from E₁?
2. Suppose the external source has a power of 100 W. What would be the rate of photon emission?

Answer 1

(1) To start the laser, the molecule will have to be excited from E₁ to E₃. The wavelength required is

λ = `("hc")/(Delta"E")`

= `(1.24 xx 10^(-6))/2.95`

= 420.3 nm

Laser transition takes place between E₁ and E₂. So the wavelength of the beam of laser-produced will be

λ = `("hc")/(Delta"E")`

= `(1.24 xx 10^(-6))/1.78`

= 696.6 nm

(2) energy of photon = 1.78 eV

= 1.78 × 1.602 × 10^-19 J

= 2.8516 × 10^-19 J

photons emitted per second = `"power (energy emitted per second)"/"energy of each photon"`

= `(100  "W")/(2.8516 xx 10^(-19) "J")`

= 3.506 × 10²⁰