So, this was the first inconsistency of the wave theory with the experiments. By how much would the stopping potential for a given photosensitive surface go up if the frequency of the incident radiations were to be increased from 41015 Hz to 8  1015 Hz? Ans. What is the implication of your answer? The ultraviolet light generated inside the tube falls on the walls, where magnesium tungstate gives blue light and zinc beryllium silicate gives yellow orange light. Lect 03: Wave Nature of Matter- De Broglie hypothesis. Click here. Apply quantum ideas for understanding the operation and working principle of optoelectronic devices. 22.Light of intensity falls on a sodium photo-cell of surface area. Important Topics: Important topics from Dual Nature of Radiation and Matter for boards are Planck's idea, Hertz and Lenard's Experiment, Threshold Frequency and Wave Function. Which probe has greater energy? In the relativistic domain, mass is given as: Hence, the radius of the circular path is given as: 14.An electron gun with its collector at a potential of 100 V fires out electrons in a spherical bulb containing hydrogen gas at low pressure of Hg). Would a neutron beam of the same energy be equally suitable? The first type of scattered wave has same wavelength (λ, ) as the incoming X-rays, while second type has a longer wavelength (λ) than incident rays (First type of X-rays are called unmodified x-rays, while second type of X-rays are called modified X-rays.) Assume that the frequency of the radiation incident on a metal plate is greater than its threshold frequency. This λ is called de-Broglie wavelength & it is defined as : where m is the mass of matter particle & these waves are called matter waves. (a) The minimum amount of energy required to take out an electron from the surface of metal. (e) The energy and momentum of an electron are related to the frequency and wavelength of the associated matter wave by the relations: But while the value of  is physically significant, the value of  (and therefore, the value of the phase speed ) has no physical significance. Wave theory didn’t talk about the relation between stopping potential and the threshold frequency.It said only increasing the intensity could overcome the stopping potential. Click here. 9. When quinine sulphate is illuminated with ultraviolet or violet light it gives out blue light. (iii) Photoelectric current is directly proportional to the intensity of incident radiations, provided the given frequency is greater than the threshold frequency. Electrons are collected at anode A, constituting a current in the circuit. (b) a neutron, would have the same de Broglie wavelength. If V is negative then, photoelectrons are repelled by negative cathode and only those electrons reaches anode, who have energy equal to or greater than eV. As you have seen in Exercise 11.31, an electron beam of this energy is suitable for crystal diffraction experiments. Ans. This strongly suggests that the electrons have a wavelength λ associated with them and that the. If this energy is greater than the, φ is the minimum energy required to remove the electron from metal surface. To get an X-ray of 27.6 keV, the incident electrons must possess at least 27.6 keV of kinetic electric energy. 3. of emitted electrons be greater? If we take an electron, mass=9.1 X 10-31 kg, moving with the speed of light (3 X 108 m/s). Their KE ranges from zero to E. which depends on frequency of incident radiation and nature of cathode. (The path can be viewed because the gas ions in the path focus the beam by attracting electrons, and emitting light by electron capture; this method is known as the ‘fine beam tube’ method. De Broglie wavelength is given by the relation: This wavelength is nearly 105 times less than the wavelength of yellow light. Dual Nature of Radiation and Matter ( All ) Select Topic. Following are some important and useful applications of X-rays. In which of the case will K.E. Find the (a) Maximum frequency, and (b) Minimum wavelength of X-rays produced by 30 kV electrons. Since  so electron being lighter will have more wavelengths. . The maximum energy of a photon is given as: Therefore, the maximum energy of an X-ray photon is 27.6 keV. : Since X-rays can penetrate through various materials, they are used in industry to detect defects in metallic structures in big machines, railway tracks and bridges. Hence, it is impossible to find the position of the wave. Cylinder with fine hole along its axisconnected to the battery so that electrons entering it could be accelerated to high speed. Photoelectric work function of a metal is 1eV. The transitions of electrons from various outer shells to the innermost ‘K’ shell produces a group of X-rays lines called as K-series. What is the kinetic energy of (a) fastest (b) the slowest photoelectron? For 1 marker and MCQ for class 12 boards, conceptual questions from these topics as well as threshold frequency and wave function can be asked. Hence explain why a fast neutron beam needs to be the rmalised with the environment before it can be used for neutron diffraction experiments. The first discovery of this phenomenon was made by Hertz. 10. Nuclei ( All ) Select Topic. Find, Ans.Wavelength of an electron and a photon. Click here. Ans. (a) Wavelength produced by an X-ray tube. a) Using Einstein’s photoelectric equation: Kmax = hv – Φo = (6.6×10-34×6×1014)J – (2.14×10-19)J. b) Stopping potential is given by the equation: c) Maximum speed of emitted electrons can be found using maximum kinetic energy equation: 2)Question:  Light of wavelength 488nm is incident on an emitter plate. Threshold frequency – The minimum values of frequency of the incident light below which photoelectric emission is not possible is called as threshold frequency. Here I is the intensity after penetrating the material through distance x and I, The coefficient of absorption (μ) of the material is given by. How will the following change, if the incident radiation is doubled? As the negative potential of collector rises, photoelectric current falls. Ignore the small initial speeds of the electrons. If each of these metals is exposed to radiations of wavelength 3300nm, which of these will not exit photoelectrons and why? Thus, the resolving power of an electron microscope is nearly 105times that of an optical microscope. (b) minimum wavelength of X-rays produced by 30 kV electrons. 18.Ultraviolet light of wavelength 2271 ¦ from a 100 W mercury source irradiates a photo-cell made of molybdenum metal. Diffraction maximum of electrons accelerated with 54 volt is obtained at θ = 50º for the Nickel crystal. CALL OR Whatsapp: 9394949438 ClearExam, 2nd Floor, Office No. (), Therefore, the wavelength associated with each -ray is. (a) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of 500 V with respect to the emitter. For every metal, there exists a certain minimum frequency below which no photoelectric effect occurs. Predict the new stopping voltage. To download notes, click here NOW: http://bit.ly/2ZdyFyGUnacademy JEE brings you another JEE Physics session to prepare you for JEE Mains 2020. The wavelength of the continuous X-rays spectra are independent of material. If V is the accelerating voltage applied then : If E is the energy of the particle, then. 15.The photoelectric cut-off voltage in a certain experiment is 1.5 V. What is the maximum kinetic energy of photoelectrons emitted? De Broglie wavelength of an electron is given as: Hence, the de Broglie wavelength is much greater than the given inter-electron separation. . 1.The following table gives the values of work functions for a few sensitive metals. The energy emitted by a photon is given as: Let n be the total number of photons falling per second, per unit area of the pupil. 14. Millikan repeated these measurements on thousands of drops and he found that the charge q calculated for each drop was some integral multiple of an elementary charge e. (e = 1.6 × 10. The dual nature of matter and the dual nature of radiation were revolutionary concepts of physics. Mathematically, if   p = fixed  , Then, Δp→0, Δx→∞. Question: Monochromatic light of wavelength 632.8nm is generated by a helium-neon laser having power of 9.42mW. At the beginning of the twentieth century, scientists unravelled one of the best-kept secrets of nature – the wave particle duality or the dual nature of matter and radiation. From the Einstein’s photoelectric equation, following points are clear: Here, vo = frequency of incident light, Φo = work function of metal, The relation between stopping potential, maximum kinetic energy and the frequency of incident light could be expressed mathematically as follows: using Einstein’s photoelectric equation. (b) De Broglie wavelength of an electron accelerating through a potential V, is given by the relation: Therefore, the de Broglie wavelength of each electron is 0.1639 nm. The characteristic X-rays spectra helps us to identify the element of target material. (d) Every metal has a definite work function. The relation for the de Broglie wavelength is given as: Therefore, the de Broglie wavelength of the neutron is 0.146 nm. The spectra of this group consists of several radiations with specific sharp wavelengths and frequency similar to the spectrum (line) of atoms like hydrogen. b) Work function is always fixed for a given material. 7.Draw a graph showing the variation of stopping potential with frequency of the incident radiations. (a) The momentum of an elementary particle is given by de Broglie relation: It is clear that momentum depends only on the wavelength of the particle. The frequency of emitted radiation (i.e. 27. Electrons are emitted from surface almost instantaneously (less than 10. sec after the surface illumination), even at low intensity of incident light (classically we assume that the electrons would require some time to absorb the incident light before they acquire enough kinetic energy to escape from metal). Do radiations have properties resembling a wave, a particle, or both? : The X-rays of high frequency or low wavelength are said to be hard X-rays. What is the velocity of the effected photoelectron? Deflected by electric and magnetic fields, Produce highly penetrating secondary radiation when suddenly stopped, In fig. Hence work function of is (4.17eV) which is greater than the energy of the incident radiation (= 3.76 eV) so  will not emit photoelectrons. 1. Photoelectrons are emitted with a maximum speed of 7105m/s from a surface when light of frequency 81014Hz is incident on it. Dual nature of radiation: Wave theory of electromagnetic radiation explains the phenomenon of interference, diffraction, and polarisation. Which the intensity of X-rays reveal that X-rays are produced dual nature of radiation shape the. ( retarding potential ) with respect to the tissues of body ( cells are and. Radiation needed to cause photoelectric emission from the surface of the metal, the. 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