The eyes of certain member of the reptile family pass a single visual signal to the brain when the visual receptors are struck by photons of wavelength `850nm`. If a total energy of `3.15xx10^(14)J` is required to trip the signal. What is the minimum number of photons that must strike the receptor?

Explanation

To solve the problem of determining the minimum number of photons that must strike the receptor, we can follow these steps:

### Step 1: Calculate the energy of a single photon
The energy (E) of a single photon can be calculated using the formula:

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

Where:
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\))
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\))
- \(\lambda\) is the wavelength of the photon (in meters). Given \(\lambda = 850 \, \text{nm} = 850 \times 10^{-9} \, \text{m}\).

### Step 2: Substitute the values into the formula
Substituting the values into the energy formula:

\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.00 \times 10^8 \, \text{m/s})}{850 \times 10^{-9} \, \text{m}} \]

### Step 3: Perform the calculation
Calculating the energy:

\[ E = \frac{(6.626 \times 10^{-34}) \times (3.00 \times 10^8)}{850 \times 10^{-9}} \]

\[ E \approx 2.33 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the total number of photons required
Now, we need to find the minimum number of photons (n) required to achieve the total energy of \(3.15 \times 10^{-14} \, \text{J}\). This can be calculated using the formula:

\[ n = \frac{\text{Total Energy}}{\text{Energy of one photon}} = \frac{3.15 \times 10^{-14} \, \text{J}}{2.33 \times 10^{-19} \, \text{J}} \]

### Step 5: Perform the division
Calculating the number of photons:

\[ n \approx \frac{3.15 \times 10^{-14}}{2.33 \times 10^{-19}} \approx 1.35 \times 10^5 \]

### Step 6: Round off the answer
Rounding off the number gives us:

\[ n \approx 1.37 \times 10^5 \, \text{photons} \]

### Final Answer
Thus, the minimum number of photons that must strike the receptor is approximately:

\[ \boxed{1.37 \times 10^5} \]