Question

A pulsed laser is constructed with a ruby crystal as the active element. The Ruby rod contains typically a total of 3 x 1019 Cr 3+ ions. If the laser emits light at 6943 A0wavelength, find the a. the energy of the emitted              photon in (eV) b. the total energy available per laser pulse (assuming total population inversion​

Answer 1

Answer:

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Answer 2

Answer:

A pulsed laser is constructed with Ruby crystal,

a) the energy of the photon emitted is 1.79eV

b) the total energy available per laser pulse is 8.6J.

Explanation:

Step 1:

Given a pulsed laser is constructed with a Ruby crystal. The number of $Cr^{3+}$ ions is given as $3 \times 10^{19}$. The emitted light has a wavelength $6943 \AA$.

To find the energy of emitted photon we use,

        $E=h\nu \ where \ 'h' \ is \ Planck's \ constant \ and \ \nu \ frequency \ of \ emitted \ light \\ \nu \lambda=c \ where\ 'c'\ is\ speed\ of\ light\\\nu = \frac{c}{\lambda}\\ E= \frac{hc}{\lambda}$

Step 2:

Substituting the value of wavelength we get,

$E= \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{6943 \times 10^{-10}} \ J$

To get the value of energy in eV we divide the above expression by 'e' the electronic charge.

$E(eV)= \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{6943 \times 10^{-10} \times 1.6 \times 10^{-19}} \\E= 1.79 eV$

Step 3:

Energy per pulse is given by, the energy of one photon multiplied by the number of atoms in the excited state.

Energy per pulse = $1.79 \times 3 \times 10^{19} \ eV$

Energy per pulse (in Joules) = $1.79 \times 3 \times 10^{19} \times 1.6 \times 10^{-19} = 8.6 \ J$

Therefore,

a) the energy of the photon emitted is 1.79eV

b) the total energy available per laser pulse is 8.6J.