Photoelectric Effects and deBroglie Equation: Practice Problem & Solution
A photoelectric surface is illuminated successively by monochromatic light of wavelength $\lambda$ and $\lambda/2$. If the maximum kinetic energy of the emitted photoelectrons in the second case is 3 times that in the first case, the work function of the surface of the material is: ($h$ = Plank's constant, $c$ = speed of light) (2015 Re)
Short Solution (Best for NEET):
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:
Let K be the initial kinetic energy. $\frac{hc}{\lambda} = W + K$ and $\frac{hc}{\lambda/2} = \frac{2hc}{\lambda} = W + 3K$. Multiplying the first equation by 3 gives $\frac{3hc}{\lambda} = 3W + 3K$. Subtracting the second equation from this gives $\frac{hc}{\lambda} = 2W$. Therefore, the work function is $W = \frac{hc}{2\lambda}$.
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