Question

A laser is used in eye surgery to weld a detached retina back into place. The wavelength of the laser beam is 537 nm, while the power is 2.0 W. During surgery, the laser beam is turned on for 0.050 s. During this time, how many photons are emitted by the laser?

Answer 1

Answer:

No. of photons, n = $2.688\times 10^{17}$

Given:

wavelength of laser beam, $\lambda = 537 nm = 537\times 10^{-9} m$

Power of the beam, P = 2.0 W

Time, t = 0.050 s

Solution:

Now the energy associated with the beam, $E_{b}$ is given by:

$E_{b} = \frac{hc}{\lambda }$                 (1)

where,

h = $6.67\times 10^{-34} J-s$

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

Now, using eqn (1)

$E_{b} = \frac{6.67\times 10^{-34} \times 3\times 10^{8}}{537\times 10^{-9}} = 3.72\time 10^{-19} J$

Now, for total energy, E' calculation from the given power:

E' = $P\times t$

E' = $2.0\times 0.050 = 0.1 J$

To calculate  the no. of photons, n:

n = $\frac{Total energy}{Energy associated with laser beam}$

n = $\frac{E'}{E_{b}}$

n = $\frac{0.1}{3.72\times 10^{-19}}$

Therefore, the no. of photons emitted by the laser beam:

n = $2.688\times 10^{17}$