For a metal of work function 6.6 ~eV$6.6 \mathrm{~eV}$, which of the following wavelengths of incident radiation does not give rise to the photoelectric effect? (Take Planck's constant as 6.6 × 10⁻³⁴ ~J s$6.6 \times 10^{-34} \mathrm{~J\ s}$)

Core Logic

Evaluate each match logically based on fundamental physics concepts:

A. E = hν$E = h\nu$ represents the discrete energy of a photon (Match IV).

B. Diffraction and interference are classical phenomena that directly confirm the wave nature of light (Match III).

C. λ = (h)/(p)$\lambda = \frac{h}{p}$ is the fundamental de Broglie wavelength equation defining the wave nature of particles (Match I).

D. The Compton effect involves the scattering of a photon by a charged particle, confirming the particle nature of light (Match II).

Step 1: Final Conclusion

Combining the logical deductions: A arrow$\rightarrow$ IV B arrow$\rightarrow$ III C arrow$\rightarrow$ I D arrow$\rightarrow$ II

Pattern Recognition

Standard concept mapping: Interference = waves; Compton/Photoelectric = particles; E=hν$E=h\nu$ = photon energy; λ=h/p$\lambda=h/p$ = matter waves.

Chapter Mix

Class 12 Physics: Dual Nature of Radiation and Matter Class 12 Physics: Wave Optics