JEE Main 2025 Apr 7 Shift 1, Chemistry Q7: Dual Character Of Matter And Radiation

Threshold frequency ${\nu }_0=5.16\times 10^{14}$ Hz corresponds to threshold wavelength

${\lambda }_0=\frac{c}{{\nu }_0}=\frac{3\times 10^8}{5.16\times 10^{14}}\approx 5.81\times 10^{-7}$ m $\approx 581$ nm

Light of wavelength shorter than 581 nm (frequency higher than ${\nu }_0$) can eject photoelectrons.

Evaluating each statement:

A. Yellow light spans roughly 570$-$590 nm, which is at or below the threshold wavelength, so it produces a current. Correct.

B. Reducing intensity of an above-threshold light decreases the number of photons per second and hence the photocurrent. Correct.

C. Red light ($\sim$620$-$750 nm) has wavelength greater than 581 nm, so its photon energy is below the work function and no current flows, regardless of brightness. Incorrect.

D. Blue light ($\sim$450$-$490 nm) has shorter wavelength than yellow, so its photon energy exceeds the work function and a current is produced. Correct.

E. White light is a mixture of all visible wavelengths, including blue and yellow components that exceed the threshold, so a current flows. Correct.

$\therefore$ Correct statements are A, B, D and E $\Rightarrow$ Option (4).