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}}. \]
If $ \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p $, then $ 96 \log_e p $ is equal to _______