The relationship between energy (E) of wavelength `2000 A^(0) and 8000 A^(0)` , respectively is

Options

A. `E_1 = 4 E_2`
B. `E_1=2E_2`
C. `E_1=(E_2)/2`
D. `E_1=(E_2)/4`

Answer

To find the relationship between the energies (E) corresponding to the wavelengths of 2000 Å and 8000 Å, we can use the formula that relates energy and wavelength:

### Step-by-Step Solution:

1. **Understanding the Relationship**: According to Planck's theory, the energy (E) of a photon is inversely proportional to its wavelength (λ). This can be expressed mathematically as:
\[ E \propto \frac{1}{\lambda} \]
This means that as the wavelength increases, the energy decreases.

2. **Setting Up the Equation**: For two different wavelengths (λ1 and λ2), we can write the relationship between their energies (E1 and E2) as:
\[ \frac{E1}{E2} = \frac{\lambda2}{\lambda1} \]

3. **Substituting the Values**: Here, we have:
- λ1 = 2000 Å
- λ2 = 8000 Å

Substituting these values into the equation gives:
\[ \frac{E1}{E2} = \frac{8000}{2000} \]

4. **Calculating the Ratio**: Simplifying the right side:
\[ \frac{8000}{2000} = 4 \]
Therefore, we have:
\[ \frac{E1}{E2} = 4 \]

5. **Expressing E1 in Terms of E2**: This implies that:
\[ E1 = 4 \times E2 \]

### Conclusion:
The relationship between the energies corresponding to the wavelengths of 2000 Å and 8000 Å is:
\[ E1 = 4 \times E2 \]