Which of the following statements are correct, if the threshold frequency of caesium is $ 5.16 \times 10^{14} \, \text{Hz} $?
In the photoelectric effect, electrons are ejected from a material when light of a frequency greater than the threshold frequency strikes it.
Option A: When yellow light (which has a frequency greater than the threshold frequency) is focused on caesium, electrons are ejected, and current flows. Therefore, this statement is correct.
Option B: Dimming the brightness of the yellow light reduces the number of photons, which in turn decreases the number of electrons ejected. Hence, the current in the ammeter is reduced. This statement is correct.
Option C: Red light has a frequency lower than the threshold frequency of caesium, so it does not have enough energy to eject electrons. Hence, no current will be produced. This statement is incorrect.
Option D: Blue light has a frequency greater than the threshold frequency, so it will eject electrons and form current in the ammeter. This statement is correct.
Thus, the correct answer is B, C, and D Only.
Einstein's Explanation of the Photoelectric Effect:
Einstein explained the photoelectric effect on the basis of Planck’s quantum theory, where light travels in the form of small bundles of energy called photons.
The energy of each photon is hν, where:
The number of photons in a beam of light determines the intensity of the incident light.When a photon strikes a metal surface, it transfers its total energy hν to a free electron in the metal.A part of this energy is used to eject the electron from the metal, and this required energy is called the work function.The remaining energy is carried by the ejected electron as its kinetic energy.
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: