JEE Physics Dual Nature Of Radiation And Matter Notes Set 01

Photoelectric Effect

1. Light of frequency above a threshold \( \nu_0 \) ejects electrons from a metal almost instantly. Einstein's equation is \( h\nu=\phi+K_{max} \) with \( \phi=h\nu_0 \). The stopping potential satisfies \( eV_0=K_{max} \), and a graph of \( V_0 \) against \( \nu \) has slope \( h/e \) for every metal.
2. The photocurrent is proportional to intensity (number of photons per second), while the maximum kinetic energy does not depend on intensity. Photons carry energy \( h\nu=1240/\lambda\ (\text{eV nm}) \) and momentum \( h/\lambda \). Doubling the frequency gives more than double the kinetic energy.

Radiation Pressure

1. A beam of intensity I exerts a pressure I/c on an absorbing surface and 2I/c on a perfect reflector. The number of photons per second is power divided by photon energy, and for the same power it is proportional to the wavelength.

de Broglie Waves

1. A moving particle has wavelength \( \lambda=h/p=h/\sqrt{2mK} \). For a charge q accelerated through V, \( \lambda=h/\sqrt{2mqV} \); for an electron \( \lambda=12.27/\sqrt V \) Å. At the same kinetic energy a lighter particle has the longer wavelength.
2. For a thermal particle \( \lambda=h/\sqrt{3mkT} \). In Bohr's first orbit the de Broglie wavelength equals the circumference of the orbit, and \( n\lambda=2\pi r \) in the nth orbit.

Davisson-Germer Experiment

1. Electrons from a heated filament are accelerated by a voltage, scattered from a nickel crystal and detected; the peak intensity at a particular angle for 54 V gave a wavelength agreeing with h/p and proved the wave nature of electrons. The speed of the electrons is controlled by the accelerating voltage and not by the filament current.

Relativistic Mass

1. The mass of a moving body is \( m=m_0/\sqrt{1-v^2/c^2} \); the mass doubles at \( v=c\sqrt3/2 \). For very fast electrons the wavelength is \( h/mv \) with this relativistic mass.