The photoelectric effect is described by Einstein's photoelectric equation: \[ h\nu = \phi + \text{KE}_{\text{max}}, \] where:
\( h \nu \) is the energy of the incident photon,
\( \phi \) is the work function (minimum energy required to emit an electron),
\( \text{KE}_{\text{max}} \) is the maximum kinetic energy of the emitted photoelectrons.
Analysis of statements:
\( A: \) True. The photocurrent (number of photoelectrons emitted per second) is proportional to the intensity of the incident radiation, which determines the number of photons.
\( B: \) False. The maximum kinetic energy of photoelectrons depends on the frequency, not the intensity.
\( C: \) True. The maximum kinetic energy depends on the frequency of the incident light (\( \nu \)) through the equation \( \text{KE}_{\text{max}} = h\nu - \phi \).
\( D: \) False. The emission of photoelectrons depends on the frequency of the light exceeding the threshold frequency, not intensity.
\( E: \) False. The maximum kinetic energy depends on the frequency.
Final Answer: The correct statements are: \[ \boxed{\text{(3) \( A \) and \( C \) only}}. \]
Given below are two statements: one is labelled as Assertion (A) and the other one is labelled as Reason (R).
Assertion (A): Emission of electrons in the photoelectric effect can be suppressed by applying a sufficiently negative electron potential to the photoemissive substance.
Reason (R): A negative electric potential, which stops the emission of electrons from the surface of a photoemissive substance, varies linearly with the frequency of incident radiation.
In light of the above statements, choose the most appropriate answer from the options given below:

Which of the following statements are correct, if the threshold frequency of caesium is $ 5.16 \times 10^{14} \, \text{Hz} $?

Let \( a \in \mathbb{R} \) and \( A \) be a matrix of order \( 3 \times 3 \) such that \( \det(A) = -4 \) and \[ A + I = \begin{bmatrix} 1 & a & 1 \\ 2 & 1 & 0 \\ a & 1 & 2 \end{bmatrix} \] where \( I \) is the identity matrix of order \( 3 \times 3 \).
If \( \det\left( (a + 1) \cdot \text{adj}\left( (a - 1) A \right) \right) \) is \( 2^m 3^n \), \( m, n \in \{ 0, 1, 2, \dots, 20 \} \), then \( m + n \) is equal to: