The ratio of energy of photon of `lambda = 2000 Å` to that of `lambda = 4000 Å` is

Options

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

Explanation

To find the ratio of the energy of photons with wavelengths \( \lambda_1 = 2000 \, \text{Å} \) and \( \lambda_2 = 4000 \, \text{Å} \), we can use the formula for the energy of a photon:

\[ E = \frac{hc}{\lambda} \]

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 (\( 3 \times 10^8 \, \text{m/s} \)),
- \( \lambda \) is the wavelength.

### Step 1: Write the energy expressions for both wavelengths
The energy of the photon for \( \lambda_1 \) (2000 Å) is:

\[ E_1 = \frac{hc}{\lambda_1} \]

The energy of the photon for \( \lambda_2 \) (4000 Å) is:

\[ E_2 = \frac{hc}{\lambda_2} \]

### Step 2: Find the ratio of the energies
Now, we can find the ratio of the energies \( \frac{E_1}{E_2} \):

\[ \frac{E_1}{E_2} = \frac{\frac{hc}{\lambda_1}}{\frac{hc}{\lambda_2}} = \frac{\lambda_2}{\lambda_1} \]

### Step 3: Substitute the values of the wavelengths
Substituting \( \lambda_1 = 2000 \, \text{Å} \) and \( \lambda_2 = 4000 \, \text{Å} \):

\[ \frac{E_1}{E_2} = \frac{4000 \, \text{Å}}{2000 \, \text{Å}} = 2 \]

### Conclusion
Thus, the ratio of the energy of the photon of \( \lambda = 2000 \, \text{Å} \) to that of \( \lambda = 4000 \, \text{Å} \) is:

\[ \frac{E_1}{E_2} = 2 \]

### Final Answer
The answer is \( 2 \).

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