Define photoelectric effect and explain the experimental set-up of the photoelectric effect.
The photoelectric effect refers to the emission of electrons from a material (usually a metal) when exposed to light of a sufficiently high frequency. This phenomenon provides evidence for the particle nature of light, as photons transfer energy to electrons.
Experimental Set-Up:
The experimental setup to observe the photoelectric effect typically includes:
- A light source (e.g., UV light) with a known frequency.
- A photosensitive material (metal plate) connected to an electrometer.
- A variable voltage source to control the stopping potential.
- A collector to capture the emitted photoelectrons.
The light is directed onto the metal surface, and the emitted electrons are detected by the electrometer.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]