Photoelectric Effects and deBroglie Equation: Practice Problem & Solution
A source $S_1$ is producing $10^{15}$ photons per second of wavelength $5000 \mathring{A}$. Another source $S_2$ is producing $1.02 \times 10^{15}$ photons per second of wavelength $5100 \mathring{A}$. Then (power of $S_2$)/(power of $S_1$) is equal to: (2010 Pre)
Solution Explained:
To solve this problem, we apply the core principles of Photoelectric Effects and deBroglie Equation. Understanding the underlying formula is key to arriving at the correct answer below:
Power is given by $P = \frac{n h c}{\lambda}$, where n is the number of photons emitted per second. Thus, $\frac{P_2}{P_1} = \frac{n_2 / \lambda_2}{n_1 / \lambda_1} = \left(\frac{n_2}{n_1}\right) \left(\frac{\lambda_1}{\lambda_2}\right) = \left(\frac{1.02 \times 10^{15}}{10^{15}}\right) \left(\frac{5000}{5100}\right) = 1.02 \times \frac{50}{51} = 1.00$.
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