An atom absorb `2eV`energy and is excited to next energy state . The wavelength of light absorbed will be

Options

A. `2000A^(@)`
B. `4000A^(@)`
C. `8000A^(@)`
D. `6206A^(@)`

Explanation

To find the wavelength of light absorbed by an atom when it absorbs 2 eV of energy and gets excited to the next energy state, we can use the formula that relates energy and wavelength:

### 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 (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength in meters.

2. **Convert energy from electron volts to joules**:
The energy given is 2 eV. To convert this to joules, we use the conversion factor:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
Therefore:
\[ E = 2 \, \text{eV} = 2 \times 1.6 \times 10^{-19} \, \text{J} = 3.2 \times 10^{-19} \, \text{J} \]

3. **Rearranging the formula to find wavelength**:
We can rearrange the energy-wavelength relationship to solve for wavelength:
\[ \lambda = \frac{hc}{E} \]

4. **Substituting the values**:
Now, substitute the values of \(h\), \(c\), and \(E\) into the equation:
\[ \lambda = \frac{(6.626 \times 10^{-34} \, \text{Js})(3.00 \times 10^8 \, \text{m/s})}{3.2 \times 10^{-19} \, \text{J}} \]

5. **Calculating the wavelength**:
Performing the calculation:
\[ \lambda = \frac{1.9878 \times 10^{-25}}{3.2 \times 10^{-19}} \approx 6.20625 \times 10^{-7} \, \text{m} \]

6. **Convert to nanometers**:
To express the wavelength in nanometers (nm), we convert meters to nanometers:
\[ 1 \, \text{m} = 10^9 \, \text{nm} \]
Therefore:
\[ \lambda \approx 6.20625 \times 10^{-7} \, \text{m} \times 10^9 \, \text{nm/m} \approx 620.625 \, \text{nm} \]

7. **Final answer**:
The wavelength of light absorbed by the atom is approximately \(620.625 \, \text{nm}\).