Question

38.1 the photon, the quantum of light
under ideal conditions, the human eye can detect light of wavelength 550 nm if as few as 100 photons/s are absorbed by the retina. at what rate is energy absorbed by the retina?
○ 3.6 w
○ 3.6 × 10⁻¹⁷ w
○ 3.6 × 10⁻²⁶ w
○ 3.6 × 10⁻¹⁹ w
○ 3.6 × 10⁻²⁸ w

Explanation:

Step1: Recall Photon Energy Formula

The energy of a single photon is given by \( E = \frac{hc}{\lambda} \), where \( h = 6.626\times10^{-34}\, \text{J·s} \) (Planck's constant), \( c = 3\times10^{8}\, \text{m/s} \) (speed of light), and \( \lambda \) is the wavelength.

Step2: Convert Wavelength to Meters

Given \( \lambda = 550\, \text{nm} = 550\times10^{-9}\, \text{m} = 5.5\times10^{-7}\, \text{m} \).

Step3: Calculate Single Photon Energy

Substitute values into \( E = \frac{hc}{\lambda} \):
\( E = \frac{(6.626\times10^{-34}\, \text{J·s})(3\times10^{8}\, \text{m/s})}{5.5\times10^{-7}\, \text{m}} \approx 3.616\times10^{-19}\, \text{J} \).

Step4: Calculate Energy Rate (Power)

Rate of energy absorption is power \( P = \text{number of photons per second} \times \text{energy per photon} \).
Given 100 photons/s, so \( P = 100 \times 3.616\times10^{-19}\, \text{J/s} \approx 3.6\times10^{-17}\, \text{W} \).

Answer:

\( 3.6\times 10^{-17}\, \text{W} \) (corresponding to the option "3.6×10⁻¹⁷ W")