Suppose `10^(-17)J` of light energy is needed by the interior of the human eye to see an object. How many photons of green light `(lambda=550nm)` are needed to generate this minimum amount of energy?

Explanation

To determine how many photons of green light (with a wavelength of 550 nm) are needed to generate an energy of \(10^{-17} J\), we can use the formula for the energy of a photon:

\[ E = \frac{hc}{\lambda} \]

Where:
- \(E\) is the energy of a single photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} J \cdot s\)),
- \(c\) is the speed of light (\(3.00 \times 10^8 m/s\)),
- \(\lambda\) is the wavelength of light (in meters).

### Step 1: Convert the wavelength from nanometers to meters
The wavelength given is \(550 nm\). To convert this to meters:

\[ \lambda = 550 \, nm = 550 \times 10^{-9} \, m \]

### Step 2: Calculate the energy of a single photon
Using the formula \(E = \frac{hc}{\lambda}\):

\[ E = \frac{(6.626 \times 10^{-34} \, J \cdot s)(3.00 \times 10^8 \, m/s)}{550 \times 10^{-9} \, m} \]

Calculating this gives:

\[ E = \frac{(6.626 \times 3.00) \times 10^{-34 + 8 + 9}}{550} \]

\[ E = \frac{19.878 \times 10^{-17}}{550} \approx 3.61 \times 10^{-19} \, J \]

### Step 3: Calculate the number of photons needed
Now, we need to find out how many photons are required to generate \(10^{-17} J\) of energy. We can use the formula:

\[ n = \frac{E_{total}}{E_{photon}} \]

Where:
- \(E_{total} = 10^{-17} J\)
- \(E_{photon} \approx 3.61 \times 10^{-19} J\)

Substituting the values:

\[ n = \frac{10^{-17}}{3.61 \times 10^{-19}} \approx 27.7 \]

Since the number of photons must be a whole number, we round this to:

\[ n \approx 28 \]

### Final Answer:
The number of photons needed is approximately **28**.