Photoelectric Effects and deBroglie Equation: Practice Problem & Solution
Assertion (A): By de-Broglie hypothesis, \(p = h/\lambda\) for both the electron and the photon. Reason (R): If an electron has the same wavelength as a photon, they have the same energy.
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:
Concept: De Broglie wavelength and energy relations.
Formula: De Broglie wavelength \(\lambda = h/p\). Photon energy \(E_p = pc = hc/\lambda\). Electron kinetic energy \(E_e = p^2/(2m) = h^2/(2m\lambda^2)\) (non-relativistic).
Solution: De Broglie's hypothesis states that momentum \(p = h/\lambda\) applies to all particles, including electrons and photons. So (A) is true. If an electron and a photon have the same wavelength, their energies are \(E_p = hc/\lambda\) and \(E_e = h^2/(2m\lambda^2)\), which are generally not equal. So (R) is false.
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