Assume that `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 = 495nm)` are needed to generate this minimum energy .
`[h=6.6xx10^(-34) Js]`

Answer

To solve the problem, we need to determine how many photons of green light (with a wavelength of 495 nm) are required to generate a minimum energy of \(10^{-17}\) J.

### Step-by-Step Solution:

1. **Understand the Energy of a Single Photon**:
The energy \(E\) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(h = 6.6 \times 10^{-34} \, \text{Js}\) (Planck's constant),
- \(c = 3 \times 10^8 \, \text{m/s}\) (speed of light),
- \(\lambda = 495 \, \text{nm} = 495 \times 10^{-9} \, \text{m}\) (wavelength of green light).

2. **Calculate the Energy of a Single Photon**:
Substitute the values into the formula:
\[ E = \frac{(6.6 \times 10^{-34} \, \text{Js})(3 \times 10^8 \, \text{m/s})}{495 \times 10^{-9} \, \text{m}} \]

Now, calculate the numerator:
\[ 6.6 \times 10^{-34} \times 3 \times 10^8 = 1.98 \times 10^{-25} \, \text{Jm} \]

Now, divide by the wavelength:
\[ E = \frac{1.98 \times 10^{-25}}{495 \times 10^{-9}} \approx 4.00 \times 10^{-19} \, \text{J} \]

3. **Determine the Number of Photons Needed**:
To find the number of photons \(N\) required to generate the minimum energy \(E_{\text{total}} = 10^{-17} \, \text{J}\), use the formula:
\[ N = \frac{E_{\text{total}}}{E} \]
Substitute the values:
\[ N = \frac{10^{-17}}{4.00 \times 10^{-19}} \approx 25 \]

### Final Answer:
The number of photons of green light needed to generate the minimum energy is approximately **25**.

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