Question

A 193nm-wavelength UV laser for eye surgery emits a 0.500mJ pulse. (a) How many photons does the light pulse contain?

Answer 1

Find the frequency of the wave.

$$ f=\frac{c}{\lambda} $$

Here, the frequency of the wave is \(f,\) speed of light is \(c,\) and the wavelength of the wave is \(\lambda\).

 

Substitute \(3 \times 10^{8} \mathrm{~m} / \mathrm{s}\) for \(c,\) and \(193 \times 10^{-9} \mathrm{~m}\) for \(\lambda\)

$$ \begin{aligned} f &=\frac{3 \times 10^{8}}{193 \times 10^{-9}} \\ &=1.55 \times 10^{15} \mathrm{~Hz} \end{aligned} $$

Find the energy of the photon.

$$ E_{\text {phatan}}=h f $$

Here, energy of the photon is \(E_{\text {photan}}\), and Planck's constant is \(h\).

Substitute \(6.626 \times 10^{-34} \mathrm{~J}_{. \mathrm{S}}\) for \(h,\) and \(1.55 \times 10^{15} \mathrm{~Hz}\) for \(f\)

$$ \begin{aligned} E_{\text {phaton}} &=6.626 \times 10^{-34} \times 1.55 \times 10^{15} \\ &=1.03 \times 10^{-18} \mathrm{~J} \end{aligned} $$

 

Find the number of photon in the pulse.

\(n=\frac{E}{E_{\text {photan}}}\)

Here, number of photon in the pulse is \(n,\) and the energy of the photon is \(E\).

Substitute \(1.03 \times 10^{-18}\) J for \(E_{p h b a n n}\), and \(0.5 \times 10^{-3}\) J for \(E\).

\(n=\frac{0.5 \times 10^{-3}}{1.03 \times 10^{-18}}\)

\(=4.87 \times 10^{14}\)

Hence, the number of photon is \(4.87 \times 10^{14}\)