Which of the following statements are correct, if the threshold frequency of caesium is 5.16 × 10¹⁴ Hz ?
A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs , the ammeter shows the presence of current.
B. When the brightness of the yellow light is dimmed, the value of the current in the ammeter is reduced.
C. When a red light is used instead of the yellow light, the current produced is higher with respect to the yellow light.
D. When a blue light is used, the ammeter shows the formation of current.
E. When a white light is used. the ammeter shows formation of current.
Choose the correct answer from the options given below:

Solution

Chemistry ma’am · 3 steps

Turn the threshold frequency into a wavelength, about 581 nm, and check each colour against it.

1. Threshold wavelength. Electrons leave caesium only if the light's frequency is at least ν₀. That means the wavelength must be at most λ₀ = c/ν₀.

   λ₀ = (3.0 × 10⁸ m s⁻¹)/(5.16 × 10¹⁴ s⁻¹) = 5.81 × 10⁻⁷ m ≈ 581 nm

   Light	Wavelength (approx.)	Frequency	Current?
   Yellow (A)	about 575 nm	5.22 × 10¹⁴ Hz, just above ν₀	yes
   Red (C)	about 700 nm	4.29 × 10¹⁴ Hz, below ν₀	no
   Blue (D)	about 450 nm	6.67 × 10¹⁴ Hz, above ν₀	yes
   White (E)	400 to 750 nm	contains blue, green and yellow	yes

2. Brightness. Dimming the yellow light lowers its intensity, so fewer photons strike the metal each second. Fewer electrons are ejected, so the current falls and B is correct. Brightness does not change the energy of each photon.
3. So. A, B, D and E are correct. C is wrong because red light gives no current at all, so the answer is (c).

The idea to keep. In the photoelectric effect, frequency decides whether electrons come out at all. Intensity decides how many come out, and so the size of the current.

Answer from the NTA final answer key. Solution by PrepWiser.