Calculate the energy of one of the photons of a beam of light having wavelength `25.0 mu m.`

Explanation

To calculate the energy of one photon of a beam of light with a wavelength of 25.0 µm, we can use the formula:

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

where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\)),
- \(c\) is the speed of light in vacuum (\(3.0 \times 10^{8} \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters.

### Step-by-Step Solution:

1. **Convert the wavelength from micrometers to meters**:
\[ \lambda = 25.0 \, \mu m = 25.0 \times 10^{-6} \, m \]

2. **Substitute the values into the energy formula**:
\[ E = \frac{(6.626 \times 10^{-34} \, \text{J s}) \times (3.0 \times 10^{8} \, \text{m/s})}{25.0 \times 10^{-6} \, m} \]

3. **Calculate the numerator**:
\[ (6.626 \times 10^{-34}) \times (3.0 \times 10^{8}) = 1.9878 \times 10^{-25} \, \text{J m} \]

4. **Now divide by the wavelength**:
\[ E = \frac{1.9878 \times 10^{-25} \, \text{J m}}{25.0 \times 10^{-6} \, m} \]

5. **Perform the division**:
\[ E = 7.9512 \times 10^{-21} \, \text{J} \]

6. **Round the answer**:
\[ E \approx 7.95 \times 10^{-21} \, \text{J} \]

### Final Answer:
The energy of one photon of a beam of light with a wavelength of 25.0 µm is approximately \(7.95 \times 10^{-21} \, \text{J}\).