Question:medium

Which of the following statement is correct?

Show Hint

In the photoelectric effect, frequency acts as a threshold switch. If $v < v_0$, no emission occurs regardless of intensity. If $v > v_0$, photoelectrons are ejected instantly, and increasing the frequency further increases their kinetic energy linearly.
Updated On: May 20, 2026
  • Photon has momentum as well as wavelength, but electrons do not have momentum and wavelength
  • In photoelectric effect if frequency $v > v_0$, then photoelectrons are ejected with certain kinetic energy
  • Azimuthal Quantum number explains about spatial orientation of orbital
  • Heisenberg uncertainty principle can be applied to all the objects and for macroscopic objects the uncertainty is extremely large
Show Solution

The Correct Option is B

Solution and Explanation

Understanding the Concept: The photoelectric effect describes the emission of electrons from a metal surface when light shines on it. According to Einstein's photoelectric equation: \[ h v = h v_0 + K_{\text{max}} \implies K_{\text{max}} = h(v - v_0) \] where $v$ is the incident frequency and $v_0$ is the threshold frequency characteristic of the metal surface. Emission occurs only if the energy of the incident photon exceeds the work function of the metal ($v>v_0$).
Step 1: Evaluate Statement (B).
Einstein's equation shows that when the frequency of the incident radiation is higher than the threshold frequency ($v>v_0$), emission occurs instantly. The remaining energy of the photon is converted into the kinetic energy of the ejected photoelectron ($K_{\text{max}}>0$). This makes statement (B) a correct description of the phenomenon.
Step 2: Verify why the other choices contain scientific errors.

Statement (A) is incorrect: According to de Broglie's hypothesis, moving material particles like electrons exhibit dual wave-particle character and possess a matter wavelength given by $\lambda = \frac{h}{p}$.
Statement (C) is incorrect: The azimuthal quantum number ($l$) dictates the subshell type and shape of the orbital. Spatial orientation is determined by the magnetic quantum number ($m_l$).
Statement (D) is incorrect: For macroscopic large bodies, because mass is huge, the uncertainty product ($\Delta x \cdot \Delta v \ge \frac{h}{4\pi m}$) becomes completely negligible and unmeasurable.
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