Question

A ruby laser emits an intense pulse of light that lasts a mere $10ns$. The light has a wavelength of $690nm$, and each pulse has an energy of $500mJ$.

a. How many photons are emitted in each pulse?

b. What is the rate of photon emission, in photons per second, during the$10ns$ that the laser is “on”?

Short answer

a. The photons are emitted in each pulse is $1.74\times {10}^{18}$.

b. The rate of photon emission, in photons per second, during the$10ns$is$1.74\times {10}^{26}\frac{photon}{s}$.

Step-by-step solution

Part (a) step 1: Given Information

We need to find photons are emitted in each pulse.

Part (a) step 2: Simplify

We can start the solution with the total energy of the pulse as:

$\begin{array}{rr}{E}_{net}& =N{E}_{ph}\\ E_{ph}& =\frac{hc}{\lambda }\\ N& =\frac{E_{net}}{E_{ph}}\\ N& =\frac{E_{net}\lambda }{hc}\\ N& =\frac{500\times {10}^{-3}\times 690\times {10}^{-9}}{6.63\times {10}^{-34}\times 3\times {10}^8}\\ N& =1.74\times {10}^{18}\end{array}$

Part (b) step 1: Given Information

We need to find the rate of photon emission, in photons per second, during the$10ns$.

Part (b) step 2: Simplify

Now, use the definition of the rate of emission:

$$\begin{gathered} R=\frac{N}{t} \\ R=\frac{1.74\times {10}^{18}}{10\times {10}^{-9}} \\ R=1.74\times {10}^{26}\frac{photons}{s} \end{gathered}$$