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}}. \]
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: