Matter Waves de Broglie & Davisson-Germer — Practice Questions

Free NEET Physics multiple-choice questions on Matter Waves de Broglie & Davisson-Germer. Attempt each question and reveal the answer with a full explanation.

According to the de-Broglie hypothesis, the plot of the de-Broglie wavelength versus the momentum p of a particle is a: Rectangular hyperbola Straight line passing through the origin Parabola Circle An electron of mass m e and a proton of mass m p are moving with the same momentum. The ratio of their de-Broglie wavelengths e / p is: 1 m p / m e m e / m p m p / m e The de-Broglie wavelength of a Helium atom at temperature T is . The de-Broglie wavelength of a Neon atom at the same temperature T is (Atomic mass of He = 4 , Ne = 20 ): / 5 5 / 5 5 The uncertainty in position of an electron ( m = 9.1 10 -31 kg ) is 1 10 -10 m . The uncertainty in its momentum is approximately: 5.27 10 -25 kg m/s 1.05 10 -24 kg m/s 3.31 10 -24 kg m/s 6.62 10 -25 kg m/s The de-Broglie wavelength of an electron moving in the second Bohr orbit of Hydrogen atom is (where a 0 is Bohr radius): 4 a 0 2 a 0 a 0 8 a 0 A proton and an -particle are accelerated from rest through the same potential difference V . The ratio of their de-Broglie wavelengths p / is: 8 : 1 2 : 1 1 : 2 1 : 8 The de-Broglie wavelength of a neutron at 927 C is . Its wavelength at 27 C will be: 2 /2 4 /4 A proton and an electron have the same de-Broglie wavelength. If K p and K e are their kinetic energies respectively, then: K e > K p K e < K p K e = K p K e = 1836 K p The de-Broglie wavelength of an electron in the n=3 state of a hydrogen atom is 3 . The de-Broglie wavelength in the ground state ( n=1 ) is 1 . The ratio 3 / 1 is: 3 1/3 9 1/9 If the de-Broglie wavelength of a proton and an -particle are in the ratio 2:1 , the ratio of their velocities v p : v is: 2:1 1:2 8:1 1:8 The de-Broglie wavelength of an electron moving with kinetic energy E is . If its kinetic energy becomes E + E , the new wavelength is /2 . The value of E is: 3E 4E 2E E In a Davisson-Germer experiment, the angle between the incident beam and the scattered beam is 50 . The glancing angle with the atomic planes is: 65 25 40 50 An electron and a photon each have a wavelength of 1.00 nm . The ratio of their momenta is: 1 1.5 2.0 0.5 The de-Broglie wavelength of a thermal neutron at temperature T K is . At what temperature will its wavelength be /2 ? 4T 2T T/4 16T The uncertainty in position of an electron is 10 -10 m and that of a proton is 10 -10 m . The ratio of minimum uncertainty in their velocities v e / v p is approximately: 1836 1 1/1836 1836 A proton and an -particle are moving with the same de-Broglie wavelength. The ratio of their kinetic energies E p / E is: 4:1 1:4 2:1 1:2 If the momentum of a particle is increased by 100 % , the percentage decrease in its de-Broglie wavelength is: 50 % 100 % 25 % 75 % The wavelength e of an electron and p of a photon of same energy E are related by p e 2 p e p e p 1 e An electron of mass m and a photon have same energy E . The ratio of de-Broglie wavelengths associated with them is : 1 c ( E 2m ) 1/2 ( E 2m ) 1/2 c(2mE) 1/2 1 xc ( 2m E ) 1/2 An electron of mass m with an initial velocity V =V 0 i ( V 0 > 0 ) enters an electric field E =-E 0 i ( E 0 = constant > 0 ) at t = 0. If 0 is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is 0 t 0 (1+ eE 0 mV 0 t ) 0 (1+ eE 0 mV 0 t ) 0 De-Broglie wavelength of an electron orbiting in the n = 2 state of hydrogen atom is close to (Given Bohr radius = 0.052 nm) 2.67 nm 0.067 nm 0.67 nm 1.67 nm A photon and an electron (mass m ) have the same energy E . The ratio ( photon / electron ) of their de Broglie wavelengths is: ( c is the speed of light) 1 c E 2m E 2m c 2mE c 2m E A particle of mass 1 mg has the same wavelength as an electron moving with a velocity of 3 10 6 m/s . The velocity of the particle is: ( m e = 9.1 10 -31 kg ) 2.7 10 -21 m/s 2.7 10 -18 m/s 3 10 -31 m/s 9 10 -2 m/s The de-Broglie wavelength of an electron accelerated through a potential of 100 V is approximately: 1.227 12.27 0.1227 122.7 The energy of a photon of wavelength k is E . A particle of mass m has the same de-Broglie wavelength k . The kinetic energy of the particle is: E 2 k / (2hc 2) E 2 / (2mc 2) 2mc 2 / E E / (2mc 2) The uncertainty in the position of an electron is equal to its de-Broglie wavelength. The minimum uncertainty in its velocity is: v/2 v/4 v h/m In the Davisson-Germer experiment, if the accelerating voltage is increased from 44 V to 54 V , the location of the maximum intensity peak: Shifts to a smaller scattering angle Shifts to a larger scattering angle Remains at the same angle Disappears The de-Broglie wavelength of an electron in the first excited state of hydrogen atom is ( a 0 is Bohr radius): 4 a 0 2 a 0 a 0 8 a 0 A particle of mass m is moving in a horizontal circle of radius r under a centripetal force -k/r 2 . The de-Broglie wavelength of the particle is: h mr/k h k/mr h/ mkr h m/kr An electron of mass m with an initial velocity v = v 0 i ( v 0 > 0 ) enters an electric field E = -E 0 i ( E 0 = constant > 0 ) at t = 0 . If 0 is its de-Broglie wavelength initially, then its de-Broglie wavelength at time t is: 0 ( 1 + e E 0 t m v 0 ) -1 0 ( 1 + e E 0 t m v 0 ) 0 t 0 The de-Broglie wavelength of a neutron at room temperature 27 C is . What will be its de-Broglie wavelength at 127 C ? 3 /2 2/3 /2 2 If the uncertainty in the position and momentum of a particle are equal, then the uncertainty in its velocity will be: 1 2m h h 1 m h 1 2m h 2 An electron and a photon have the same energy E . The ratio of their de-Broglie wavelengths e/ ph is ( c is speed of light): 1 c E 2m c 2m E E 2mc 2 2m E If an electron and a photon have the same de-Broglie wavelength of 1 nm , which of the following is true regarding their energies? Energy of photon is greater than kinetic energy of electron Energy of photon is less than kinetic energy of electron They have equal energies Energy of photon is half of kinetic energy of electron If the kinetic energy of a free electron is tripled, its de-Broglie wavelength changes by a factor of: 1/ 3 3 3 1/3 In the Davisson-Germer experiment, the maximum intensity is observed when the scattering angle and the glancing angle are related such that: = 90 - /2 = = /2 = 180 - If the uncertainty in the velocity of an electron is 5.7 10 5 m/s , the uncertainty in its position is approximately: ( h = 6.63 10 -34 J s , m e = 9 10 -31 kg ) 10 -10 m 10 -12 m 10 -8 m 10 -7 m If the de-Broglie wavelength of an electron is equal to the radius of the first Bohr orbit of a hydrogen atom ( 0.53 ), what is its velocity? ( h = 6.6 10 -34 J s ) 1.37 10 7 m/s 2.18 10 6 m/s 3.28 10 5 m/s 4.12 10 8 m/s An electron is moving with an initial velocity v = v 0 i . An electric field E = E 0 j is switched on. The de-Broglie wavelength of the electron at time t is: 0 / 1 + (eE 0t/mv 0) 2 0 (1 + eE 0t/mv 0) 0 0 / (1 + eE 0t/mv 0) If a particle of mass m is moving in a region where the potential energy is zero, the de-Broglie wavelength is . If it enters a region where the potential energy is U , the new wavelength will be: E / (E - U) (E - U) / E (E - U) / E E / (E - U) A photon and an electron, each of 20 eV energy, move in free space. The ratio of linear momentum of electron p e to that of photon p ph , p e p ph , is: [Take speed of light =3 10 8 ms -1 , charge of electron =-1.6 10 -19 C and mass of electron =9 10 -31 kg] 2 450 1 250 225 275 Which of the following figures represents the variation of particle momentum and the associated de-Broglie wavelength? Rectangular hyperbola Linear passing through origin Parabola Circle An electron and a proton are accelerated through the same potential difference. Which one has the higher velocity? Electron Proton Both have same velocity Cannot be determined A proton and an -particle are accelerated through the same potential difference V . The ratio of their de-Broglie wavelengths p/ is: 8 : 1 1 : 8 2 : 1 1 : 2 Which of the following figures correctly represents the variation of particle momentum ( p ) with its de-Broglie wavelength ( )? A rectangular hyperbola A straight line passing through origin A parabola An exponential curve In Davisson-Germer experiment, the maximum intensity of scattered electrons is observed at a scattering angle of: 50 30 90 45 The de-Broglie wavelength associated with an electron accelerated through a potential V is . If the potential is changed to V/4 , the new wavelength will be: 2 /2 4 /4 The de-Broglie wavelength of a particle of mass m and charge q accelerated from rest through a potential V is: h/ 2mqV h/ mqV 2mqV/h 2mqV /h The de-Broglie wavelength of a ball of mass 0.12 kg moving with a speed of 20 m/s is ( h = 6.6 10 -34 J s ): 2.75 10 -34 m 2.75 10 -35 m 0.12 10 -34 m 3.3 10 -34 m A particle of mass m and charge q is accelerated from rest through a potential difference V . Its de-Broglie wavelength is: h 2mqV h mqV 2mqV h h mqV Which of the following has the smallest de-Broglie wavelength when all move with the same velocity? Alpha particle Proton Electron Neutron Two particles of mass m 1 and m 2 have equal kinetic energies. The ratio of their de-Broglie wavelengths 1/ 2 is: m 2/m 1 m 1/m 2 m 2/m 1 m 1/m 2 A proton and an -particle are moving with the same velocity. The ratio of their de-Broglie wavelengths p / is: 4 : 1 1 : 4 2 : 1 1 : 2 An electron, a proton, and an alpha particle have the same kinetic energy. Which of them has the longest de-Broglie wavelength? Electron Proton Alpha particle All have same wavelength A particle moves in a closed loop. If its de-Broglie wavelength is , then the circumference of the n th stable orbit must be: n /n 2n n 2 The de-Broglie wavelength of an electron is 0.1 nm . The potential difference through which it was accelerated is approximately: 150 V 12 V 1000 V 1.5 V The wave nature of matter is not observed in daily life because: The de-Broglie wavelength is very small The speed of macro objects is very high Planck's constant is very large Macro objects do not possess momentum Davisson and Germer experiment proved: Wave nature of electrons Particle nature of electrons Wave nature of light Particle nature of light A particle of mass m has a de-Broglie wavelength . If its velocity is reduced to half, the new wavelength will be: 2 /2 4 /4 If a proton and an -particle are moving with the same momentum, the ratio of their de-Broglie wavelengths p : is: 1 : 1 1 : 2 2 : 1 4 : 1 The de-Broglie wavelength of an electron moving with kinetic energy E is . If the kinetic energy is reduced to E/9 , the new de-Broglie wavelength will be: 3 9 /3 /9 An atom of mass M initially at rest emits a photon of wavelength . The recoil velocity of the atom is: h M h M M h hc M Which property of the electron is used in an electron microscope? Wave nature Particle nature Negative charge Spin Which of the following is the correct graph between the de-Broglie wavelength and the accelerating potential V for an electron? V -1/2 V V 2 V 1/2 If the Planck's constant h were to double, the de-Broglie wavelength of a fixed-mass particle moving with a fixed kinetic energy would: Double Become four times Remain unchanged Be halved If the kinetic energy of a particle is 100 eV and its de-Broglie wavelength is 1 , what will be its de-Broglie wavelength when its kinetic energy becomes 400 eV ? 0.5 2 0.25 4 A particle of mass m is moving with a constant velocity v . If its de-Broglie wavelength is , its kinetic energy is: h 2 2m 2 h 2 2m h 2m 2 hm 2 2 The ratio of de-Broglie wavelength of a photon and an electron of same momentum p is: 1:1 1:2 2:1 Depends on energy Which of the following graphs correctly represents the variation of the de-Broglie wavelength ( ) of a particle with its kinetic energy ( K )? A curve where decreases as K increases (rectangular hyperbola style). A straight line with positive slope. A straight line with negative slope. A parabola opening upwards. Which particle will have the highest momentum if all move with the same de-Broglie wavelength? All will have the same momentum Electron Proton Alpha particle The de-Broglie wavelength of a ball of mass 100 g moving with a velocity of 33 m/s is: ( h = 6.6 10 -34 J s ) 2 10 -34 m 2 10 -33 m 2 10 -35 m 6.6 10 -34 m The de-Broglie wavelength of an electron is the same as that of a photon. If is the wavelength, the ratio of the momentum of the electron to that of the photon is: 1:1 1:2 2:1 1:4 The resolving power of an electron microscope is much higher than that of an optical microscope because: The wavelength of electrons is much smaller than that of visible light Electrons have more energy than light photons Electrons are charged particles Magnetic lenses used are very powerful The de-Broglie wavelength of a proton and an alpha particle are equal. The ratio of their velocities v p : v is: 4:1 1:4 2:1 1:2 A proton, a deuteron and an alpha particle are accelerated through the same potential difference. The ratio of their kinetic energies is: 1:1:2 1:1:1 1:2:4 2:1:1 In the Davisson-Germer experiment, the maximum intensity is observed when electrons are accelerated through 54 V at a scattering angle of: 50 45 60 90 Which of the following is the correct expression for the de-Broglie wavelength of a particle of mass m and kinetic energy K ? h/ 2mK 2mK /h h/2mK h 2mK A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct? Diffraction pattern is not observed on the screen in the case of electrons The angular width of the central maximum of the diffraction pattern will increase The angular width of the central maximum will decrease The angular width of the central maximum will be unaffected If the kinetic energy of the particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is :- 25 75 60 50 If the mass of neutron is 1.7 10 -27 kg , then the de-Broglie wavelength of neutron of energy 3eV is : (h=6.6 10 -34 Js ) 1.4 10 -11 m 1.6 10 -10 m 1.65 10 -11 m 1.4 10 -10 m If the kinetic energy of a particle is increased to 4 times, its de-Broglie wavelength becomes: Half Double Four times One-fourth An electron is accelerated through a potential difference of 10 , 000 V . Its de Broglie wavelength is, (nearly) : (m e=9 10 -31 kg ) 12.2 nm 12.2 10 -13 m 12.2 10 -12 m 12.2 10 -14 m An electron is accelerated from rest through a potential difference of V volt. If the de Broglie wavelength of the electron is 1.227 10 -2 nm , the potential difference is : 10 2 V 10 3 V 10 4 V 10 V The graph which shows the variation of the de Broglie wavelength ( ) of a particle and its associated momentum ( p ) is The graph which shows the variation of ( 1 2 ) and its kinetic energy, E is (where is de Broglie wavelength of a free particle): Match List I with List II. array llll ; & List-I & ; & List-II A. & E = h & I. & de Broglie wavelength B. & Diffraction and Interference & II. & Particle nature of light C. & = h/p & III. & Wave nature of light D. & Compton effect & IV. & Energy of photon array Choose the correct answer from the options given below. A-IV, B-III, C-II, D-I A-IV, B-III, C-I, D-II A-I, B-IV, C-III, D-II A-IV, B-I, C-II, D-III An electron is accelerated through a potential difference of 10,000 V . Its de-Broglie wavelength is, nearly ( m e = 9 10 -31 kg ): 12.27 10 -12 m 12.27 10 -10 m 12.27 10 -9 m 12.27 10 -8 m An alpha particle and a proton are accelerated from rest by the same potential. The ratio of their de-Broglie wavelengths / p is: 1 / 2 2 1 / 2 1 / 2 1 If the kinetic energy of a free electron doubles, its de-Broglie wavelength changes by the factor: 1 / 2 2 1/2 2 The de-Broglie wavelength of an electron moving with a velocity c/100 is: 2.4 10 -10 m 2.4 10 -12 m 2.4 10 -9 m 2.4 10 -8 m The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (Kelvin) and mass m is: h 3mkT h mkT h 2mkT 2h 3mkT For which of the following particles moving with the same velocity is the de-Broglie wavelength maximum? -particle Proton Neutron -particle A particle of mass M at rest decays into two particles of masses m 1 and m 2 having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles 1 / 2 is: 1 m 2/m 1 m 1/m 2 m 2/m 1 If the momentum of an electron is changed by p , then the de-Broglie wavelength associated with it changes by 0.5 % . The initial momentum of the electron was: 200 p 400 p 100 p p/200 A proton and an -particle are accelerated from rest to the same kinetic energy. The ratio of their de-Broglie wavelengths p : is: 2 : 1 1 : 2 1 : 1 4 : 1 The de-Broglie wavelength of an electron in the 4th Bohr orbit of Hydrogen atom is related to the radius of the orbit r 4 as: = r 4 2 = 2 r 4 = 4 r 4 = r 4 4 An electron of mass m and a photon have the same energy E . The ratio of the de-Broglie wavelength of the electron to that of the photon is ( c being the velocity of light): 1 c ( E 2m ) 1/2 1 c ( 2m E ) 1/2 ( E 2m ) 1/2 c (2mE) 1/2 If the kinetic energy of a particle is increased to 16 times its previous value, the percentage change in the de-Broglie wavelength of the particle is: 75 % 25 % 50 % 60 % An electron is moving with a speed of v . If its de-Broglie wavelength is equal to the wavelength of a photon of frequency , then the speed v is given by: h mc h m 2h mc mc 2 h If a particle's position is measured with an uncertainty of 10 -10 m , the minimum uncertainty in its momentum is approximately ( h = 6.63 10 -34 J s ): 0.5 10 -24 kg m/s 1.0 10 -24 kg m/s 6.6 10 -44 kg m/s 3.3 10 -24 kg m/s An electron is accelerated through a potential difference of 64 V . What is the de-Broglie wavelength of the electron? 1.53 12.27 1.23 0.12 A particle of mass m is moving in a circular path of radius r such that its centripetal acceleration is a c . The de-Broglie wavelength associated with the particle is: h / m 2 a c r h / m a c r h r / m a c h / m a c The de-Broglie wavelength of an atom of mass M in thermal equilibrium with its surroundings at temperature T is proportional to: (MT) -1/2 (MT) 1/2 M 1/2 T -1/2 MT -1 The de-Broglie wavelength of an electron moving in the n th orbit of a hydrogen atom is: Directly proportional to n Inversely proportional to n Directly proportional to n 2 Inversely proportional to n 2 If the de-Broglie wavelength of an electron is 1.227 , then the accelerating potential is: 100 V 10 V 1000 V 50 V The de-Broglie wavelength of a gas molecule of mass m at temperature T (Kelvin) is proportional to: 1 / mT T / m m/T T / m A beam of electrons is used in a Young's double-slit experiment. If the speed of the electrons is increased, the fringe width will: Decrease Increase Remain same Fringes will disappear If a proton and an electron have the same de-Broglie wavelength, then the ratio of their kinetic energies K p / K e is: m e / m p m p / m e m e / m p 1 A particle of mass m and charge q is accelerated through a potential V . A second particle of mass 2m and charge q is accelerated through the same potential. The ratio of their de-Broglie wavelengths is: 2 : 1 1 : 2 2 : 1 1 : 2 The de-Broglie wavelength of a thermal neutron at temperature 27 C is . What will be its de-Broglie wavelength at 927 C ? /2 /4 2 /3 If the uncertainty in the position of an electron is equal to its Bohr radius a 0 , the uncertainty in its momentum p is: h/(2 a 0) h/a 0 h/(4 a 0) 2 h/a 0 The de-Broglie wavelength of an electron accelerated through a potential V is . The de-Broglie wavelength of a proton accelerated through the same potential V will be (where M p is mass of proton and m e is mass of electron): m e/M p M p/m e (m e/M p) (M p/m e) Which of the following transitions in a hydrogen atom will emit a photon of the shortest de-Broglie wavelength? n=2 to n=1 n=4 to n=3 n=3 to n=2 n=4 to n=2 Which of the following graphs represents the variation of de-Broglie wavelength with the momentum p of a particle? Rectangular hyperbola Straight line passing through origin Parabola Circle The ratio of the de-Broglie wavelength of a proton and an -particle, both moving with the same kinetic energy, is: 2:1 1:2 4:1 1:4 Which of the following particles will have the largest de-Broglie wavelength when accelerated through the same potential difference? Electron Proton -particle Deuteron If a photon and an electron have the same energy E , then the ratio of their wavelengths photon / electron is proportional to: 1/ E E E E 2 The de-Broglie wavelength of an electron moving with speed v is . If the speed is increased by 25 % , the new de-Broglie wavelength is: 0.8 1.25 0.75 0.4 In a Davisson-Germer experiment, if the distance between atomic planes of the crystal is d , the condition for constructive interference for electrons with wavelength scattered at angle with the plane is: 2d = n d = n 2d = n d = n An electron and a deuteron have the same de-Broglie wavelength. The ratio of their kinetic energies K e/K d is ( m d is mass of deuteron, m e is mass of electron): m d/m e m e/m d m d/m e m e/m d The de-Broglie wavelength of an electron in the ground state of the hydrogen atom is approximately: 3.3 0.53 1.06 6.6 The de-Broglie wavelength of an electron, an -particle and a proton all having the same kinetic energy are e , and p respectively. Which of the following is correct? e > p > e < p < e = p = e > > p If the uncertainty in the position of an electron is 10 -10 m , the minimum uncertainty in its velocity is approximately: ( h = 6.63 10 -34 J s , m e = 9.1 10 -31 kg ) 5.8 10 5 m/s 5.8 10 6 m/s 1.2 10 5 m/s 3.0 10 8 m/s The de-Broglie wavelength of a neutron at temperature 27 C is . If the temperature is increased to 927 C , the new de-Broglie wavelength will be: /2 /4 2 In the Davisson-Germer experiment, the maximum intensity of the scattered electron beam is observed at a scattering angle and accelerating voltage V of: = 50 , V = 54 V = 54 , V = 50 V = 45 , V = 60 V = 90 , V = 54 V A particle of mass m is moving in a potential field U = 1 2 kx 2 . The de-Broglie wavelength of the particle at its mean position, if its total energy is E , is: h 2mE h mE h m E h kE The uncertainty in the momentum of a particle is 6.63 10 -24 kg m/s . The minimum uncertainty in its position is: 0.08 0.8 8 80 The de-Broglie wavelength of an electron in the first Bohr orbit of the Hydrogen atom is: 2 a 0 a 0 a 0 / 2 4 a 0 The de-Broglie wavelength of an electron in the n th Bohr orbit of radius r is given by: 2 r / n r / n nh / 2 r 2 r n A proton and an alpha particle are accelerated through the same potential difference. The ratio of their velocities v p / v is: 2 2 2 2 1 An electron and a proton are moving with the same de-Broglie wavelength. Which of the following statements is true? The kinetic energy of the electron is greater than that of the proton. The kinetic energy of the proton is greater than that of the electron. The momentum of the electron is greater than that of the proton. Both have the same kinetic energy. A particle A of mass m and charge q , and a particle B of mass 4m and charge q are accelerated from rest by the same potential V . The ratio of their de-Broglie wavelengths A / B is: 2 1/2 4 1 If the momentum of an electron is tripled, the percentage change in its de-Broglie wavelength is: 66.7 % decrease 300 % increase 66.7 % increase 200 % decrease The de-Broglie wavelength associated with an electron accelerated through a potential V is . For a proton to have the same wavelength , it must be accelerated through a potential difference of (let m p = 1840 m e ): V / 1840 1840 V V / 1840 1840 V The de-Broglie wavelength of an electron is 1.227 10 -10 m . Its kinetic energy is approximately: 100 eV 120 eV 50 eV 10 eV