Question

A ruby laser emits an intense pulse of light that lasts a mere 10 ns. The light has a wavelength of 690 nm, and each pulse has an energy of 500 mJ. a. How many photons are emitted in each pulse? b. What is the rate of photon emission, in photons per second, during the 10 ns that the laser is “on”?

Short answer

$$\begin{gathered} a:1.735587\times {10}^{18}photons \\ b:1.735587\times {10}^{26}photons \end{gathered}$$

Step-by-step solution

Given Information

Wavelength of light: 690nm

Time of pulse: 10ns

energy per pulse: 500mJ = 0.5J

Part a:

Energy of one photon: $\frac{hc}{\lambda }$

Energy emitted in one pulse: 0.5J

No. of photons:$\frac{Energyofpulse}{Energyofphoton}$

$$\begin{gathered} =\frac{0.5J}{{\displaystyle \frac{hc}{690\times {10}^{-9}m}}} \\ =\frac{0.5J\times 690\times {10}^{-9}m}{6.626\times {10}^{-34}Js\times 3\times {10}^{8}m{s}^{-1}} \\ =1.735587\times {10}^{18}photons \end{gathered}$$

Part b:

Now for 10ns, $1.735587\times {10}^{18}$photons were emitted.

If this would have continued for 1 sec, no. of photons emitted will be

$$\begin{gathered} \frac{1sec}{10ns}\times no.ofphotonsemittedin10ns \\ =\frac{1\times {10}^{9}ns}{10ns}\times 1.735587\times {10}^{18}photons \\ =1.735587\times {10}^{26}photons \end{gathered}$$