Question

the human eye is able to detect as little as $2.35\times10^{-18} \text{j}$ of green light of wavelength $510 \text{nm}$. calculate the minimum number of photons of green light that can be detected by the human eye. consult the table of physical constants as needed. number of photons =

Explanation:

Step1: Calculate the energy of a single photon

The energy of a photon is given by the formula \(E = \frac{hc}{\lambda}\), where \(h = 6.626\times10^{-34}\space J\cdot s\) (Planck's constant), \(c = 3\times10^{8}\space m/s\) (speed of light), and \(\lambda\) is the wavelength.
First, convert the wavelength from nanometers to meters: \(\lambda=510\space nm = 510\times10^{-9}\space m\)
Substitute the values into the formula:
\(E=\frac{6.626\times 10^{-34}\times3\times 10^{8}}{510\times 10^{-9}}\)
\(E=\frac{19.878\times 10^{-26}}{510\times 10^{-9}}\)
\(E = 3.9\times10^{-19}\space J\)

Step2: Calculate the number of photons

The total energy \(E_{total}=2.35\times 10^{-18}\space J\)
The number of photons \(n=\frac{E_{total}}{E}\)
\(n=\frac{2.35\times 10^{-18}}{3.9\times 10^{-19}}\)
\(n=\frac{2.35}{3.9}\times10\)
\(n\approx6\)

Answer:

\(6\)