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 \(\left( \frac{E_1}{E_2} \right)\).
Correct Answer: 2
Solution and Explanation
Step 1: Recall the equation for the energy of a photon.
\[ E_{\text{photon}} = \frac{hc}{\lambda} \]
Step 2: Write the expression for the ratio of the energies.
\[ \frac{E_1}{E_2} = \frac{\lambda_2}{\lambda_1} \]
Step 3: Substitute the given values of wavelengths.
\[ \frac{E_1}{E_2} = \frac{6000}{3000} = 2 \]
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