Quantum Physics

Step 1: Analyze the photoelectric effect. The photoelectric effect involves the emission of electrons from a material when light shines on it. Key observations, such as the existence of a threshold frequency and the instantaneous emission of electrons, could not be explained by the wave theory of light. Albert Einstein explained it by postulating that light consists of discrete packets of energy called photons (particles). Therefore, the photoelectric effect is a primary evidence for the particle nature of light. Statement A is incorrect, and statement C is correct.
Step 2: Analyze the Compton effect. The Compton effect describes the scattering of X-rays or gamma rays by electrons. The observed change in wavelength of the scattered radiation is explained by treating the interaction as a collision between a photon and an electron, conserving both energy and momentum. This billiard-ball-like interaction is a clear demonstration of the particle nature of light. Therefore, the Compton effect exhibits the particle nature of light. Statement B is incorrect, and statement D is correct.
Step 3: Conclude which statements are correct. Both statements C and D are correct. They both point to phenomena that support the particle (photon) model of light.

Step 1: Recall the photoelectric effect equation. Einstein's photoelectric equation relates the maximum kinetic energy ( ) of a photoelectron to the frequency of the incident photon ( ) and the work function of the metal ( ): where is Planck's constant.
Step 2: Relate stopping potential to kinetic energy. The stopping potential ( ) is the potential required to stop the most energetic photoelectrons. It is related to the maximum kinetic energy by: where is the elementary charge. Combining the two equations gives:
Step 3: Analyze the dependencies of the stopping potential. From the equation, we can see that depends on: - The frequency ( ) of the incident photon. - The wavelength ( ), since . - The work function ( ), which is a property of the specific metal (type of metals). The intensity of the incident light determines the *number* of photons arriving per unit time, which in turn determines the number of photoelectrons emitted (the photoelectric current). However, it does not affect the energy of individual photons, and thus does not affect the maximum kinetic energy or the stopping potential of the photoelectrons.

Step 1: Recall the formula for the Compton shift. The Compton shift, , which is the change in wavelength of a photon after scattering off an electron, is given by: where is the scattering angle.
Step 2: Define the Compton wavelength. The Compton wavelength, , is a constant defined as:
Step 3: Set the Compton shift equal to the Compton wavelength and solve for . We are given the condition . Dividing both sides by gives: The angle for which (in the range ) is .