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