What if the energy associated with a monochreomatic ultraviolet rediation with a wavelength of `10^(-3)m`?

Explanation

To find the energy associated with monochromatic ultraviolet radiation with a wavelength of \(10^{-3}\) m, we can follow these steps:

### Step 1: Identify the given values
- Wavelength (\(\lambda\)) = \(10^{-3}\) m
- Speed of light (\(c\)) = \(3 \times 10^8\) m/s
- Planck's constant (\(h\)) = \(6.6 \times 10^{-34}\) J·s

### Step 2: Calculate the frequency (\(\nu\))
The frequency can be calculated using the formula:
\[ \nu = \frac{c}{\lambda} \]
Substituting the known values:
\[ \nu = \frac{3 \times 10^8 \text{ m/s}}{10^{-3} \text{ m}} = 3 \times 10^{11} \text{ Hz} \]

### Step 3: Calculate the energy (E)
The energy associated with the radiation can be calculated using the formula:
\[ E = h \nu \]
Substituting the values of \(h\) and \(\nu\):
\[ E = (6.6 \times 10^{-34} \text{ J·s}) \times (3 \times 10^{11} \text{ Hz}) \]
Calculating this gives:
\[ E = 19.8 \times 10^{-23} \text{ J} \]
This can be rounded to:
\[ E \approx 1.98 \times 10^{-22} \text{ J} \]

### Final Answer
The energy associated with the monochromatic ultraviolet radiation with a wavelength of \(10^{-3}\) m is approximately \(1.98 \times 10^{-22}\) joules.

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