The ratio of the energy of a photon of wavelength `3000 "Å" ` to that of photon of wavelength `6000 "Å"`is :

Options

A. `(1)/(2)`
B. 2
C. 3
D. `(1)/(3)`

Answer

To find the ratio of the energy of a photon with a wavelength of 3000 Å to that of a photon with a wavelength of 6000 Å, we can use the relationship between energy and wavelength. The energy (E) of a photon is inversely proportional to its wavelength (λ), which can be expressed with 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 photon.

### Step-by-Step Solution:

1. **Identify the wavelengths**:
- Wavelength 1 (\( \lambda_1 \)) = 3000 Å = \( 3000 \times 10^{-10} \, \text{m} \)
- Wavelength 2 (\( \lambda_2 \)) = 6000 Å = \( 6000 \times 10^{-10} \, \text{m} \)

2. **Write the energy expressions**:
- Energy of photon 1 (\( E_1 \)):
\[ E_1 = \frac{hc}{\lambda_1} \]
- Energy of photon 2 (\( E_2 \)):
\[ E_2 = \frac{hc}{\lambda_2} \]

3. **Set up the ratio of energies**:
\[ \frac{E_1}{E_2} = \frac{\frac{hc}{\lambda_1}}{\frac{hc}{\lambda_2}} = \frac{\lambda_2}{\lambda_1} \]

4. **Substitute the wavelengths**:
\[ \frac{E_1}{E_2} = \frac{6000 \, \text{Å}}{3000 \, \text{Å}} = \frac{6000}{3000} = 2 \]

5. **Conclusion**:
The ratio of the energy of a photon of wavelength 3000 Å to that of a photon of wavelength 6000 Å is:
\[ \frac{E_1}{E_2} = 2:1 \]

### Final Answer:
The ratio of the energy of a photon of wavelength 3000 Å to that of a photon of wavelength 6000 Å is **2:1**.