The number of photons of light of wavelength 7000 A equivalent to 1 J are

Options

A. `3.52 xx10^(18)`
B. `3.52 xx10^(-18)`
C. 25000
D. 50000

Answer

To solve the problem of finding the number of photons of light with a wavelength of 7000 Å (angstroms) equivalent to 1 joule, we can follow these steps:

### Step 1: Convert Wavelength from Angstroms to Meters
1 angstrom (Å) is equal to \(10^{-10}\) meters. Therefore, to convert 7000 Å to meters:
\[ \lambda = 7000 \, \text{Å} = 7000 \times 10^{-10} \, \text{m} = 7 \times 10^{-7} \, \text{m} \]

### Step 2: Use the Energy Formula for a Photon
The energy \(E\) of a single photon can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(h\) (Planck's constant) = \(6.626 \times 10^{-34} \, \text{J s}\)
- \(c\) (speed of light) = \(3 \times 10^{8} \, \text{m/s}\)
- \(\lambda\) = \(7 \times 10^{-7} \, \text{m}\)

### Step 3: Calculate the Energy of One Photon
Substituting the values into the energy formula:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3 \times 10^{8} \, \text{m/s})}{7 \times 10^{-7} \, \text{m}} \]
Calculating this gives:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{7 \times 10^{-7} \, \text{m}} = 2.8397 \times 10^{-19} \, \text{J} \]

### Step 4: Calculate the Number of Photons in 1 Joule
To find the number of photons \(n\) that make up 1 joule, we use the formula:
\[ n = \frac{\text{Total Energy}}{\text{Energy of one photon}} = \frac{1 \, \text{J}}{E} \]
Substituting the energy of one photon:
\[ n = \frac{1 \, \text{J}}{2.8397 \times 10^{-19} \, \text{J}} \approx 3.52 \times 10^{18} \]

### Conclusion
The number of photons of light with a wavelength of 7000 Å equivalent to 1 joule is approximately:
\[ n \approx 3.52 \times 10^{18} \]

### Final Answer
Thus, the answer is \(3.52 \times 10^{18}\).

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