Ncert Books Class 12 Physics Chapter 11 Free Download

The most commonly asked derivation in board exams from this chapter is that of Einstein's photoelectric equation, K_max = hν - φ₀. Another important derivation is expressing the de Broglie wavelength (λ) of an electron in terms of its accelerating potential (V), which is λ = h / √(2meV). Practising these ensures you are prepared for the theory-based questions.

In the board exam, you can expect numericals based on:

• Calculating maximum kinetic energy or stopping potential using Einstein's photoelectric equation (K_max = hν - φ₀).
• Finding the work function (φ₀), threshold frequency (ν₀), or threshold wavelength (λ₀).
• Calculating the de Broglie wavelength of particles like electrons, protons, or alpha particles, often involving their kinetic energy or accelerating potential.

Einstein's Photoelectric Equation is K_max = hν - φ₀. In this equation:

• K_max is the maximum kinetic energy of the emitted photoelectron.
• h is Planck's constant.
• ν is the frequency of the incident radiation.
• φ₀ is the work function of the metal surface.

The most important conclusion of the Davisson-Germer experiment is that it provided the first direct experimental evidence for the wave nature of electrons. The experiment showed that a beam of electrons scattered by a nickel crystal produced a diffraction pattern, similar to X-rays. This confirmed the de Broglie hypothesis and established the principle of wave-particle duality for matter.

The classical wave theory of light fails to explain the photoelectric effect on several key grounds. To secure full marks, you must mention these three contradictions:

• Existence of Threshold Frequency: Wave theory suggests that light of any frequency, if intense enough, should cause photoemission. However, experiments show that photoemission only occurs above a certain minimum or threshold frequency.
• Kinetic Energy's Dependence: According to wave theory, the kinetic energy of photoelectrons should increase with light intensity. Experimentally, the maximum kinetic energy depends only on the frequency of light, not its intensity.
• Instantaneous Process: Wave theory predicts a time lag for an electron to absorb enough energy. However, the photoelectric effect is an instantaneous process, with no observable time delay.

The de Broglie wavelength (λ) is related to kinetic energy (K) by the formula λ = h / √(2mK). When an electron is accelerated through a potential V, its kinetic energy K equals eV. Substituting this, the formula becomes λ = h / √(2meV). This derived relationship is crucial because many board exam numericals provide the accelerating potential (V) instead of momentum or velocity, making this formula essential for a quick and accurate solution.

For the CBSE board exam, a comparison should highlight these key differences:

• Rest Mass: A photon has zero rest mass, while an electron has a definite rest mass (9.1 x 10⁻³¹ kg).
• Charge: A photon is electrically neutral and is not deflected by electric or magnetic fields. An electron is negatively charged (-1.6 x 10⁻¹⁹ C) and is deflected by both fields.
• Speed: In a vacuum, a photon always travels at the speed of light (c). An electron's speed is variable and always less than c.
• Existence: A photon only exists in motion; it cannot be at rest. An electron can be at rest or in motion.

The effect of intensity on photoelectric emission is a very important concept:

• Effect on Photoelectric Current: Intensity is proportional to the number of incident photons per second. A higher intensity means more photons strike the metal, ejecting more electrons. This leads to a higher photoelectric saturation current. The relationship is directly proportional.
• Effect on Stopping Potential: The maximum kinetic energy of photoelectrons, and thus the stopping potential (V₀), depends on the energy of a single photon (E=hν), not on the number of photons. Therefore, changing the intensity has no effect on the stopping potential, provided the frequency is constant.