The photons of light having a wavelength `4000 Å` are necessary to provide `1.00 J` of energy are.

Options

A. `6.023 xx 10^23`
B. `6.023 xx 10^18`
C. `2.01 xx 10^18`
D. `2.01 xx 10^23`

Explanation

To solve the problem of how many photons of light with a wavelength of 4000 Å are necessary to provide 1.00 J of energy, we can follow these steps:

### Step 1: Convert Wavelength to Meters
The wavelength is given in angstroms (Å). We need to convert it to meters for our calculations.

\[ \text{Wavelength} (\lambda) = 4000 \, \text{Å} = 4000 \times 10^{-10} \, \text{m} = 4 \times 10^{-7} \, \text{m} \]

### Step 2: Use the Energy of a Photon Formula
The energy of a single photon can be calculated using the formula:

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

Where:
- \(E\) = energy of a single photon
- \(h\) = Planck's constant = \(6.634 \times 10^{-34} \, \text{J s}\)
- \(c\) = speed of light = \(3 \times 10^{8} \, \text{m/s}\)
- \(\lambda\) = wavelength in meters

### Step 3: Calculate the Energy of One Photon
Substituting the values into the formula:

\[ E = \frac{(6.634 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{8} \, \text{m/s})}{4 \times 10^{-7} \, \text{m}} \]

Calculating the numerator:

\[ E = \frac{1.9902 \times 10^{-25} \, \text{J m}}{4 \times 10^{-7} \, \text{m}} = 4.9755 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the Number of Photons Required
To find the number of photons (\(n\)) required to provide 1.00 J of energy, we use the formula:

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

Where:
- \(E_{\text{total}} = 1.00 \, \text{J}\)
- \(E_{\text{photon}} = 4.9755 \times 10^{-19} \, \text{J}\)

Substituting the values:

\[ n = \frac{1.00 \, \text{J}}{4.9755 \times 10^{-19} \, \text{J}} \approx 2.01 \times 10^{18} \]

### Step 5: Final Answer
The number of photons required is approximately:

\[ n \approx 2 \times 10^{18} \]