In order to break a chemical bond in the molecules of human skin, causing sunburn , a photon energy of about `3.5 eV` is required. This corresponds to wavelength in the

Options

A. infrared region
B. X-ray region
C. visible region
D. ultraviolet region

Explanation

To find the corresponding wavelength for a photon energy of about 3.5 eV, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship Between Energy and Wavelength**:
The energy (E) of a photon is related to its wavelength (λ) by the equation:
\[ E = \frac{hc}{\lambda} \]
where:
- \(E\) is the energy in joules,
- \(h\) is Planck's constant (\(6.63 \times 10^{-34} \, \text{J s}\)),
- \(c\) is the speed of light (\(3 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters.

2. **Convert Energy from Electron Volts to Joules**:
Given that the energy is \(3.5 \, \text{eV}\), we need to convert it to joules. The conversion factor is:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
Therefore:
\[ E = 3.5 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 5.6 \times 10^{-19} \, \text{J} \]

3. **Rearrange the Energy-Wavelength Equation**:
We can rearrange the equation to solve for wavelength:
\[ \lambda = \frac{hc}{E} \]

4. **Substitute Known Values**:
Now, substitute the values of \(h\), \(c\), and \(E\) into the equation:
\[ \lambda = \frac{(6.63 \times 10^{-34} \, \text{J s})(3 \times 10^8 \, \text{m/s})}{5.6 \times 10^{-19} \, \text{J}} \]

5. **Calculate the Wavelength**:
First, calculate the numerator:
\[ 6.63 \times 10^{-34} \times 3 \times 10^8 = 1.989 \times 10^{-25} \, \text{J m} \]
Now, divide by the energy:
\[ \lambda = \frac{1.989 \times 10^{-25} \, \text{J m}}{5.6 \times 10^{-19} \, \text{J}} \approx 3.55 \times 10^{-7} \, \text{m} \]

6. **Convert Wavelength to Nanometers**:
Since \(1 \, \text{m} = 10^9 \, \text{nm}\):
\[ \lambda \approx 3.55 \times 10^{-7} \, \text{m} \times 10^9 \, \text{nm/m} = 355 \, \text{nm} \]

7. **Determine the Region of the Electromagnetic Spectrum**:
The wavelength of \(355 \, \text{nm}\) falls within the ultraviolet (UV) region of the electromagnetic spectrum.

### Final Answer:
The corresponding wavelength for a photon energy of about \(3.5 \, \text{eV}\) is approximately \(355 \, \text{nm}\), which falls in the ultraviolet (UV) region.

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