Question

The approximate number of photons in a femtosecond $\left({10}^{-15}s\right)$ pulse of 600 nanometers wavelenghth light from a 10-kilowatt peak-power dye laser is

• A. ${10}^3$
• B. ${10}^7$
• C. ${10}^{11}$
• D. ${10}^{15}$
• E. ${10}^{18}$

Answer 1

Answer: (B)

${10}^7$

Number of photon, $n=\frac{TotalEnergy}{Energyduetoasinglephoton}$

Energy of a single photon, $E_{single}=\frac{hc}{\lambda }$

$h=6.63\times {10}^{-34}Js$

$c=3\times {10}^{8}m/s$

$\lambda =600nanometers=600\times {10}^{-9}m$

Energy due to a single photon = $\frac{6.63\times {10}^{-34}\times 3\times {10}^8}{600\times {10}^{-9}}=0.033\times {10}^{-17}$

Power, $P=\frac{TotalEnergy}{Time}$

$Totalenergy=P\times t$

Given,

$P=10kW={10}^{4}W$

$t={10}^{-15}sec$

$Totalenergy={10}^4\times {10}^{-15}={10}^{-11}J$

$n=\frac{TotalEnergy}{Energyduetoasinglephoton}=\frac{{10}^{-11}}{0.033\times {10}^{-17}}=30.30\times {10}^6=3\times {10}^7$

$\therefore n={10}^{7}photons(approx.)$

Hence, the correct answer is OPTION B.