Param Himalaya - परम हिमालय

Expression for de-Broglie wavelength :  According to quantum theory, the energy of a photon is given by $E = h\nu \qquad \dots (i)$ According to Einstein's mass-energy equivalence, the energy of the photon is $E = mc^2 \qquad \dots (ii)$ From equations (i) and (ii), we have, $mc^2 = h\nu$ $mc^2 = h\frac{c}{\lambda}( \because c = \nu \lambda)$ where, $\lambda$ is de-Broglie wavelength. $mc = \frac{h}{\lambda}$  $ \lambda = \frac{h}{mc} \qquad \dots (iii)$ But $mc = p$, the momentum of photon, therefore, $\lambda = \frac{h}{p} \qquad \dots (iv)$ If instead of a photon, we have a material particle of mass $m$ moving with velocity $v$, then eqn. (iii) becomes, $\lambda = \frac{h}{mv} \qquad \dots (v)$ which is the expression for de-Broglie wavelength. Conclusions. From eqn. (v), it is concluded that, (i) de-Broglie wavelength is inversely proportional to the velocity of the particle, i.e. $\lambda \propto \frac{1}{v}$. If particle moves faster, the wavelength of the wave associate...

Define Wave Nature of Matter ? Matter Waves or De-Broglie Waves The waves associated with moving material particles are known as De-Broglie waves or matter waves. According to a french physicist Louis de-Broglie, a moving material particle can be associated with a wave.In other words, a wave can guide the motion of a particle. Wave theory of electromagnetic radiation explains the phenomena of interference, diffraction and polarization. Whereas quantum theory of electromagnetic radiation successfully explains the photoelectric effect, Compton effect, black body radiation, X-ray spectra etc. This shows that, radiations have dual nature i.e. wave and quantum or particle nature. Louis de Broglie suggested that like radiations the particles like electrons, protons, neutrons etc have also dual nature. Dual nature i.e. the material particle can behave both as wave as well as particle.  His suggestion was based on the assumptions that : (i) the universe is made of particles and radiations....

What is a photon ( Particle Nature of Light )? Write the properties of a photon. When radiation interacts with matter, to cause emission of electrons, the radiation behaves as if it is made up of particles called photons. Thus, dual nature of radiation (i.e., wave and particle nature) was established. Photon is a packet of energy or quantum of energy ejected at the speed of light by an emitter. The energy of each bundle or packet or a photon is given by, $E = h\nu$ where $h$ is Planck's constant  $h= 6.63 \times 10^{-34} Js$ and $\nu$ is the frequency of radiation. Energy of $n$ photons is given by $E = nh\nu$ A source of radiation emits energy in packets when it goes from higher energy state to lower energy state and absorbs energy in packets when it goes from lower energy state to higher energy state. Properties of a Photon :  (i) A photon travels with a speed of light in vacuum (i.e. $3 \times 10^8 ms^{-1}$).} (ii) Rest mass of a photon is zero i.e. $m_0 = 0$. It means that...

Derive Einstein's Photoelectric Equation and Verify Laws of Photoelectric emission using this equation. According to Einstein, when a photon of energy $h\nu$ falls on a metal surface, the energy of the photon is used in two ways: (i) A part of photon energy is used by an electron to just cross over the surface barrier so that it may come out of the metal surface. This part of energy is equal to the work function ($\phi_0$) of the metal ; (ii) The remaining part of the photon energy is used in giving a velocity to the emitted photo electron. This part of energy is equal to the kinetic energy ($\frac{1}{2}mv^2$) of the emitted photo-electron. The process is shown in figure  According to the law of conservation of energy, $$h\nu = \phi_0 + \frac{1}{2}mv^2 \quad \dots (i)$$ If $\nu$ is just equal to threshold frequency $\nu_0$, then the free electron will just come out of the surface of metal and its kinetic energy is zero. i.e., $$h\nu_0 = \phi_0 + 0$$ $$h\nu_0 = \phi_0 \quad \dots (i...

Photoelectric effect cannot be explained on the basis of wave theory of light". Explain this statement. Photoelectric effect cannot be explained on the basis of wave theory of light because of the following reasons: [(i)] As per wave theory of light}, the electric field component ($E$) of light increases with the increase in the intensity of the light. When light falls on a metal surface, the force acting on a free electron in the metal surface increases with the increase in the intensity of the incident light ($F = -eE$). As a result of this, the kinetic energy acquired by the free electron increases with the increase in the intensity of the incident light. Contradiction : It is observed that the maximum kinetic energy acquired by photo electron ($\frac{1}{2}mv_{max}^2 = eV_0$) is same for both incident beams of different intensities $I_1$ and $I_2$ as shown in figure. This observation is contradictory to the fact explained with the help of the wave theory of light. [(ii)] As pe...

Describe an experiment to study photo-electric effect. The experimental set up to study photoelectric effect is shown in Figure :  It consists of a highly evacuated tube having two electrodes 'A' and 'C'. The electrode 'C' is a photo-sensitive emitter which emits photoelectrons when exposed to ultra-violet radiation. The electrode 'A' is a charge (or electrons) collecting plate. The tube has a side window made of quartz covered with a filter through which the incident light of desired wavelength enters the tube and falls on the photo-sensitive plate 'C'. Electrodes 'A' and 'C' are connected to a battery through a suitable reversing switch 'S'. Electrode 'A' can be brought to a positive or a negative potential with respect to electrode 'C' with the help of this switch. Procedure : Electrons are emitted when ultraviolet radiations are made to fall on photo-sensitive plate 'C'. These electrons get att...

Define and explain electron emission. Give different types of electron emissions. The phenomenon of emission of electron from a metal surface by supplying external energy is called electron emission. Explanation : In metals, the electrons in the outermost orbit of an atom are loosely bound and can move freely in all possible directions within the metal even at room temperature. These electrons in the metal are known as free electrons. These free electrons are responsible for the conductivity of a metal. However, these free electrons cannot leave the surface of the metal of their own. As soon as an electron tends to leave the metal surface, a positive charge is developed on the surface of the metal. This positive charge pulls back (or attracts) the free electron tending to leave the metal surface. This attracting force acts like a surface barrier for free electrons. The free electron can leave the metal surface only if an external energy is available to it to overcome the surface barrie...