The ratio of the energy of a photon of `200Å` wavelength radiation to that of `400Å` radiation is :

Options

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

Explanation

To find the ratio of the energy of a photon with a wavelength of 200 Å (angstroms) to that of a photon with a wavelength of 400 Å, we will 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 (\(3.00 \times 10^8 \, \text{m/s}\)),
- \( \lambda \) is the wavelength of the photon.

### Step 1: Write the expressions for the energies of the two photons.

Let:
- \( E_1 \) be the energy of the photon with a wavelength of \( 200 \, \text{Å} \),
- \( E_2 \) be the energy of the photon with a wavelength of \( 400 \, \text{Å} \).

Using the formula for energy:
\[ E_1 = \frac{hc}{\lambda_1} = \frac{hc}{200 \, \text{Å}} \]
\[ E_2 = \frac{hc}{\lambda_2} = \frac{hc}{400 \, \text{Å}} \]

### Step 2: Find the ratio of the energies.

The ratio of the energies \( \frac{E_1}{E_2} \) can be expressed as:
\[ \frac{E_1}{E_2} = \frac{\frac{hc}{\lambda_1}}{\frac{hc}{\lambda_2}} \]

### Step 3: Simplify the ratio.

Since \( hc \) is common in both the numerator and the denominator, we can cancel it out:
\[ \frac{E_1}{E_2} = \frac{\lambda_2}{\lambda_1} \]

### Step 4: Substitute the values of \( \lambda_1 \) and \( \lambda_2 \).

Now substituting the values:
- \( \lambda_1 = 200 \, \text{Å} \)
- \( \lambda_2 = 400 \, \text{Å} \)

Thus, we have:
\[ \frac{E_1}{E_2} = \frac{400 \, \text{Å}}{200 \, \text{Å}} = 2 \]

### Conclusion:

The ratio of the energy of a photon with a wavelength of \( 200 \, \text{Å} \) to that of a photon with a wavelength of \( 400 \, \text{Å} \) is:
\[ \frac{E_1}{E_2} = 2 \]

### Final Answer:
The ratio of the energy of a photon of \( 200 \, \text{Å} \) wavelength radiation to that of \( 400 \, \text{Å} \) radiation is \( 2 \).

---