Calculate the ratio of the energy of a photon of wavelength 3000 Å to that of a photon of wavelength 6000Å respectively

Answer

To calculate the ratio of the energy of a photon of wavelength 3000 Å to that of a photon of wavelength 6000 Å, 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:
- \(E\) = energy of the photon
- \(h\) = Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\))
- \(c\) = speed of light (\(3.00 \times 10^8 \, \text{m/s}\))
- \(\lambda\) = wavelength of the photon

2. **Set Up the Energies for Each Wavelength**:
- For the first photon (wavelength \( \lambda_1 = 3000 \, \text{Å} \)):
\[ E_1 = \frac{hc}{\lambda_1} = \frac{hc}{3000 \, \text{Å}} \]
- For the second photon (wavelength \( \lambda_2 = 6000 \, \text{Å} \)):
\[ E_2 = \frac{hc}{\lambda_2} = \frac{hc}{6000 \, \text{Å}} \]

3. **Calculate the Ratio of Energies**:
To find the ratio of the energies \( \frac{E_1}{E_2} \):
\[ \frac{E_1}{E_2} = \frac{\frac{hc}{3000}}{\frac{hc}{6000}} \]
Simplifying this gives:
\[ \frac{E_1}{E_2} = \frac{6000}{3000} \]

4. **Simplify the Ratio**:
\[ \frac{E_1}{E_2} = \frac{6000}{3000} = 2 \]

### 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**.

---