Question

Wavelengths of two photons are given as \(\lambda_1 = 3000 \, \text{Å}\) and \(\lambda_2 = 6000 \, \text{Å}\) respectively. Calculate the ratio of their energies \(\left( \frac{E_1}{E_2} \right)\).

Answer 1

Correct Answer: 2

Step 1: Understanding the Question:
The question asks for the ratio of the energies of two photons given their respective wavelengths.
Step 2: Key Formula or Approach:
The energy ($E$) of a photon is related to its wavelength ($\lambda$) by the equation:
\[ E = \frac{hc}{\lambda} \]
where $h$ is Planck's constant and $c$ is the speed of light.
Step 3: Detailed Explanation:
From the formula, we see that energy is inversely proportional to wavelength ($E \propto 1/\lambda$).
\[ \frac{E_1}{E_2} = \frac{\lambda_2}{\lambda_1} \]
Given:
$\lambda_1 = 3000$ \AA
$\lambda_2 = 6000$ \AA

\[ \frac{E_1}{E_2} = \frac{6000}{3000} = 2 \]
Step 4: Final Answer:
The ratio of their energies is 2.