The ratio of the energy of a photon of 2000Å wavelength radiation to that of 4000Å radiation is

Options

A. `1//4`
B. `4`
C. `1//2`
D. `2`

Answer

To solve the problem of finding the ratio of the energy of a photon of 2000 Å wavelength radiation to that of 4000 Å radiation, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Energy of a Photon**:
The energy (E) of a photon is given by the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(E\) is the energy of the photon,
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\)),
- \(c\) is the speed of light (\(3.00 \times 10^8 \, \text{m/s}\)),
- \(\lambda\) is the wavelength of the radiation.

2. **Define the Wavelengths**:
Let:
- \(\lambda_1 = 2000 \, \text{Å} = 2000 \times 10^{-10} \, \text{m}\)
- \(\lambda_2 = 4000 \, \text{Å} = 4000 \times 10^{-10} \, \text{m}\)

3. **Calculate the Energies**:
Using the formula for energy:
- For photon 1 (2000 Å):
\[ E_1 = \frac{hc}{\lambda_1} = \frac{hc}{2000 \times 10^{-10}} \]
- For photon 2 (4000 Å):
\[ E_2 = \frac{hc}{\lambda_2} = \frac{hc}{4000 \times 10^{-10}} \]

4. **Find the Ratio of Energies**:
To find the ratio of \(E_1\) to \(E_2\):
\[ \frac{E_1}{E_2} = \frac{\frac{hc}{\lambda_1}}{\frac{hc}{\lambda_2}} = \frac{\lambda_2}{\lambda_1} \]
Substituting the values of \(\lambda_1\) and \(\lambda_2\):
\[ \frac{E_1}{E_2} = \frac{4000 \times 10^{-10}}{2000 \times 10^{-10}} = \frac{4000}{2000} = 2 \]

5. **Conclusion**:
The ratio of the energy of a photon of 2000 Å wavelength radiation to that of 4000 Å radiation is:
\[ \frac{E_1}{E_2} = 2 \]

### Final Answer:
The ratio of the energy of a photon of 2000 Å wavelength radiation to that of 4000 Å radiation is **2**.

---