Wavelength of Photon vs. Electron – Rankers Physics

Photoelectric Effects and deBroglie Equation: Practice Problem & Solution

Assertion (A): A photon and an electron both have energy \(50\text{ eV}\). Both have different wavelengths. Reason (R): Wavelength depends on energy and not on mass.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

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:

For a photon, wavelength is \(\lambda_p = hc/E\). For an electron, de Broglie wavelength is \(\lambda_e = h/\sqrt{2mE}\). Since their formulas are different and \(\lambda_e\) depends on mass \(m\), their wavelengths will be different for the same energy. So (A) is true. Reason (R) is false because an electron's de Broglie wavelength depends on its mass.

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