Atomic Structure: Practice Problem & Solution
Energy levels A, B and C of a certain atom correspond to increasing values of energy i.e., $E_A < E_B < E_C$. If $\lambda_1, \lambda_2$ and $\lambda_3$ are wavelengths of radiations corresponding to transitions C to B, B to A and C to A respectively, which of the following relations is correct? (2005)
Solution Explained:
To solve this problem, we apply the core principles of Atomic Structure. Understanding the underlying formula is key to arriving at the correct answer below:
From energy conservation, $E_C - E_A = (E_C - E_B) + (E_B - E_A)$. Using $E = \frac{hc}{\lambda}$, we have $\frac{hc}{\lambda_3} = \frac{hc}{\lambda_1} + \frac{hc}{\lambda_2}$. Dividing by $hc$ gives $\frac{1}{\lambda_3} = \frac{1}{\lambda_1} + \frac{1}{\lambda_2}$, which rearranges to $\lambda_3 = \frac{\lambda_1 \lambda_2}{\lambda_1 + \lambda_2}$.
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