Question

A laser used to weld detached retinas emits light with a wavelength of 652 nm in pulses that are 20.0 ms in duration. The average power expended during each pulse is 0.600 W.
1) How much energy is in each pulse, in joules?
2)How much energy is in each pulse, in electron volts?
3)What is the energy of one photon in joules?
4)What is the energy of one photon in electron volts?
5)How many photons are in each pulse?

Answer 1

Wavelength of the light, \(\lambda=652 \mathrm{~nm}\)

$$ \begin{aligned} &=652 \mathrm{~nm}\left(\frac{1 \mathrm{~m}}{1 \times 10^{9} \mathrm{~nm}}\right) \\ &=652 \times 10^{-9} \mathrm{~m} \end{aligned} $$

time, \(t=20.0 \mathrm{~ms}\)

$$ \begin{aligned} &=20.0 \mathrm{~ms}\left(\frac{1 \mathrm{~s}}{10^{3} \mathrm{~ms}}\right) \\ &=20.0 \times 10^{-3} \mathrm{~s} \end{aligned} $$

(1) The energy in each pulse is,

$$ \begin{aligned} E &=\text { power } \times \text { time } \\ &=(0.600 \mathrm{~W})\left(20.0 \times 10^{-3} \mathrm{~s}\right) \\ &=12 \times 10^{-3} \mathrm{~J} \end{aligned} $$

2. The energy in each pulse is,

$$ \begin{aligned} E &=12 \times 10^{-3} \mathrm{~J} \\ &=12 \times 10^{-3} \mathrm{~J}\left(\frac{1 \mathrm{eV}}{1.6 \times 10^{-19} \mathrm{~J}}\right) \\ &=7.5 \times 10^{16} \mathrm{eV} \end{aligned} $$

3.The energy of the one photon is,

\(E^{\prime}=\frac{h c}{\lambda}\) \(=\frac{\left(6.625 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\right)\left(3 \times 10^{8} \mathrm{~m} / \mathrm{s}\right)}{652 \times 10^{-9} \mathrm{~m}}\) \(=3.048 \times 10^{-10} \mathrm{~J}\)

$$ \begin{aligned} E^{\prime} &=3.048 \times 10^{-19} \mathrm{~J} \\ &=\left(3.048 \times 10^{-19} \mathrm{~J}\right)\left(\frac{1 \mathrm{eV}}{1.6 \times 10^{-19} \mathrm{~J}}\right) \\ &=1.905 \mathrm{eV} \end{aligned} $$

5. The energy of the laser is equal to the product of the num ber of photons and energy of the each photon.

$$ \begin{aligned} E &=n E^{\prime} \\ n &=\frac{E}{E^{\prime}} \\ &=\frac{12 \times 10^{-3} \mathrm{~J}}{3.048 \times 10^{-19} \mathrm{~J}} \\ &=3.94 \times 10^{16} \end{aligned} $$