Title 15-modern-physics.pdf ✅

Modern Physics 1. A heavy nucleus having mass number 200 gets disintegrated into two small fragments of mass number 80 and 120 . If binding energy per nucleon for parent atom is 6.5MeV and for daughter nuclei is 7MeV and 8MeV respectively, then the energy released in the decay will be : (A) 200eV (B) − 220eV (C) 220MeV (D) 180MeV 2. A hydrogen like atom is in a higher energy level of quantum number 6. The excited atom makes a transition to first excited state by emitting photons of total energy 27.2eV. The atom from the same excited state make a transition to the second excited state by successively emitting two photons. If the energy of one photon is 4.25eV, find the energy of other photon. (A) 5.95eV (B) 6.25eV (C) 6.95eV (D) 7.80eV 3. The helium gas in an excited state makes transition from excited state of principal quantum number n = 5 to ground state. The most energetic photons have energy 52.224eV, find the energy of least energetic photons : (A) 1.224eV (B) 2.42eV (C) 3.22eV (D) 3.82eV 4. The potential difference applied to an X-ray tube is 5KV and the current through it is 3.2 mA. Then number of electrons striking the target per second is: (A) 2 × 1016 (B) 5 × 106 (C) 1 × 1017 (D) 4 × 1015 5. Electrons with de-Broglie wavelength λ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is: (A) λ0 = 2mcλ 2 h (B) λ0 = 2h mc (C) λ0 = 2m2c 2λ 3 h2 (D) λ0 = λ 6. Electrons in a sample of gas containing hydrogen like atom (Z = 3) are in fourth excited state. When photons emitted only due to transition from third excited state to second excited state are incident on a metal plate photoelectrons are ejected. The stopping potential for these photoelectrons is 4eV. Now, if only photons emitted due to transition from fourth excited state to third excited state are incident on the same metal plate, the stopping potential for the emitted photoelectrons will be approximately equal to : (A) 0.80eV (B) 0.75eV (C) 0.65eV (D) 0.55eV 7. Nuclei of radioactive element A are product at a rate ' t ', at any time t. The element A has decay constant λ. Let N be the number of nuclei of element A at any time t. At time t = t0, dN/dt is minimum. Then the number of nuclei of element A at time t = t0 is : (A) t0−λt0 2 λ 2 (B) λt0 2−2t0 λ 2 (C) 2t0−λt0 2 λ (D) t0−λt0 2 λ 8. The photon radiated from hydrogen corresponding to 2 nd line of Lyman series is absorbed by a hydrogen like atom ' X ' in 2 nd excited state. As a result the hydrogen like atom ' X ' makes a transition to n th orbit. Then : (A) X = He +. n = 4 (b) X = Li +. n = 6 (C) X = He +. n = 6 (d) X = Li ++. n = 9 9. The thermal power of a uranium reactor is 100MW. Energy released in each fission is 3.2 × 10−11 J and the average number of neutrons released per fission is 2.5 . The number of neutrons generated in unit time is :
(A) 7.8 × 1018 (B) 1.28 × 1019 (C) 3.2 × 1019 (D) 2.5 × 1018 10. The de Broglie wavelength of an electron in the first excited state of a Hydrogen atom is: [ h is Planck's constant, m is the mass of the electron, e is the charge on the electron, K = 1 4πε0 ] (A) h 2 πKme 2 (B) h 2 2πKme 2 (C) mh 2 πKe 2 (D) mh 2 2πKe 2 11. A neutron have K.E. = 15eV suffers head on collision with hydrogen atom in ground state at rest then after collision K.E. of : (Assume mass of neutron same as that of hydrogen). (A) neutron is 1.4eV (B) hydrogen is 1.4eV (C) neutron is zero (D) hydrogen is 15eV 12. Graph is drawn between photocurrent & accelerating potential, then (A) A&B will have same intensity (B) B&C will have same frequency (C) B&C will have same intensity (D) A&B will have same frequency 13. When protons of energy 4.25eV strike the surface of a metal A, the ejected photoelectrons have maximum kinetic energy TA expressed in eV and de-Broglie wavelength λA. The maximum kinetic energy of photoelectrons liberated from another metal B by photons of energy 4.70eV is TB = (TA − 1.50eV). If the de- Broglie wavelength of these photoelectrons is λB = 2λA, then: (A) The work function of A is 2.25eV (B) The work function of B is 4.20eV (C) TA = 2.00eV (D) TB = 2.75eV 14. Suppose the potential energy between electron and proton at a distance r is given by : − Ke 2 3r 3 . The application of Bohr's theory to hydrogen atom in this case will change as follows : (A) Energy in the nth orbit is proportional to n 6 (B) Energy is proportional to m−3 ( m : mass of electron) (C) Energy the n th orbit is proportional to n −2 (D) Energy is proportional to m1 ( m = mass of electron ) 15. In the Bohr's model of the hydrogen atom: (A) radius of the n th orbit is proportional to n 2 (B) the total energy of the electron in the n th orbit is inversely proportional to n (C) the angular momentum of the electron in an orbit is an integral multiple of ( h/2π) (D) the magnitude of potential energy of the electron in any orbit is greater than its kinetic energy 16. From the following equations pick out the possible nuclear fusion reactions: (A) 6C 13 + 1H 1 ⟶ 6C 14 + 4.3MeV (b) 6C 12 + 1H 1 ⟶ 7N 13 + 2MeV (C) 7 N 14 + 1H 1 ⟶ 8O 15 + 7.3MeV (D) 92U 235 + 0n 1 ⟶ 54Xe 140 + 36Sr 94 + 0n 1 + 0n 1 + γ + 200MeV 17. In an X-ray tube, the voltage applied is 20KV. The energy required to remove an electron from L shell is 19.9KeV. In the X-rays emitted by the tube : (A) minimum wavelength will be 62.1pm (B) energy of characterstic X-ray will be equal to or less than 19.9KeV (C) LαX-ray may be emitted (D) Lα X-ray will have energy 19.9KeV 18. An electron in Hydrogen atom first jumps from second excited state to first excited state and then from first excited state to ground state. Let ratio of wavelength, momentum AND energy of photons emitted in these two cases be a, b and c respectively. Then, (A) c = 1 a (B) a = 9 4 (C) b = 5 27 (D) c = 5 27 19. The radioactivity of a nucleus may be due to various reasons. An unstable nucleus emits radiations if it goes to form a stable nucleus (or
less unstable). Then the cause and result can be (A) a nucleus of excess nucleons is α active (B) an excited nucleus of excess protons is β −active (C) an excited nucleus of excess protons is β +active (D) an nucleus of excess neutrons is β −active 20. The ground state and first excited state energies of hydrogen atom are −13.6eV and −3.4eV respectively. If potential energy in ground state is taken to be zero. Then: (A) Potential energy in the first excited state would be 20.4eV (B) Total energy in the first excited state would be 23.8eV (C) Kinetic energy in the first excited state would be 3.4eV (D) Total energy in the ground state would be 13.6eV 21. Which of the following statement(s) is/are correct? (A) The rest mass of a stable nucleus is less than the sum of the rest masses of its separated nucleons (B) The rest mass of a stable nucleus is greater than the sum of the rest masses of its separated nucleons (C) In nuclear fission, energy is released by fusing two nuclei of medium mass (approximately 100amu ) (D) In nuclear fission, energy is released by fragmentation of a heavy nucleus 22. An O 16 nucleus is spherical and has a charge radius R and a volume V = 4 3 πR 3 . According to the empirical observations, the volume of the 54X 128 nucleus (assume it to be spherical) is V and radius is R ′ , Then: (A) V ′ = 8V (B) V ′ = 2V (C) R ′ = 2R (D) R ′ = 8R 23. 10gm of a radioactive element is kept in a container. The element is β-active. Then after one half-life: (molar mass of the substance is 100gm, Avogadro's number = 6 × 1023 per mole ). (A) The weight of the substance left in the container will be 5gm. (B) The weight of the active substance in the container will be nearly 10gm. (C) If all β-particles leave the container then the charge of the substance left is 4800C (D) if all β-particles leave the container then the charge of the substance left is 9600C. 24. A metallic sphere of radius r remote from all other bodies is irradiated with a radiation wavelength λ which is capable of causing photoelectric effect. (A) The maximum potential gained by the sphere will be independent of its radius (B) The net positive charge appearing on the sphere after a long time will depend on the radius of the sphere (C) The kinetic energy of the most energetic electrons emanating from the sphere will keep of declining with time (D) The kinetic energy of the most energetic electrons emanating from the sphere initially will to independent of the radius of the sphere 25. Monochromatic light of wavelength 207 nm and intensity is made to fall on a metal plate A fixed inside a vacuum tube, leading to emission of photoelectrons. The incident light makes an angle 30∘ with plate A. The surface area of plate A is 20 cm2 Another plate B is fixed inside the tube, directly facing plate A. If the potential of plate A is kept 4 V higher than plate B, the photoemission stops completely. If the potential of plate B is made higher than plate A, the photoelectric current rises, until it reaches a saturation value of 0.5 mA. Choose the correct option(s): [hc = 1242eV − nm ] (A) The work function of plate A is 4.0eV (B) The longest wavelength of light that can cause emission from plate A is 621 nm (C) When the current is at its saturation value, one electron is emitted from plate A for every 20 photons incident on it (D) Once the current reaches its saturation value, it can further be increased by decreasing the wavelength of the incident light but not by increasing its intensity 26. An electron moving in a circular path of radius r in a plane perpendicular to a uniform magnetic field of intensity B has kinetic energy K and de Broglie wavelength λ. Choose the correct option(s): [ h is Planck's constant, e is the charge on an electron] (A) λ = h √2mK (B) r = h eBλ
(C) K = eBrh 2mλ (D) r = √2mK eB 27. An electron in the ground state in a Hydrogen atom absorbs a photon of wavelength λ and transitions to a new energy level such that the radius of its orbit becomes 16 times. The change of momentum of the Hydrogen atom due to the absorption of the photon is Δpa. Choose the correct option(s): (A) The ionization energy of the electron in the new orbit is 0.85eV (B) λ = 97.4 nm (C) Δpa = 6.78 × 10−27 kg m/s (D) The electron can now transition to a lower energy level and emit a photon of wavelength 90 nm 28. Two radioactive decay processes are given below: (1) 55 137Cs → 56 137Ba 12 23Mg → 11 23Na The Q-value of these two processes, Q1 and Q2 respectively, are given by: [Here, m(X) denotes the mass of an atom of the element X, me denotes the mass of an electron, Q0 denotes the amount of energy liberated when 1u of mass converts to energy] (A) Q1 = (m(Cs) − m(Ba) − me )Q0 (B) Q1 = (m(Cs) − m(Ba))Q0 (C) Q2 = (m(Cs) − m(Ba) + 2me )Q0 (D) Q2 = (m(Mg) − m(Na) + me )Q0 29. In an experiment on X-rays, high energy electrons, all of de Broglie wavelength λe , are made to collide with target plate made of a material of atomic number Z. The minimum wavelength observed in the continuous X-ray spectrum is λm. Choose the correct option(s): (A) Wavelength of the observed Kα line is independent of λe but not independent of Z (B) Wavelength of the observed Kα line is independent of neither λe nor Z (C) The minimum wavelength observed in the continuous X-ray spectrum is independent of both λe and Z (D) The minimum wavelength observed in the continuous X-ray spectrum is independent of Z but not independent of λe 30. Consider a Bohr orbit in the Hydrogen atom with principal quantum number n(n > 1). If an electron in this orbit makes a transition to the immediately lower orbit, it emits a photon of wavelength λL and the change in momentum experienced by the Hydrogen atom due to this emission be ΔpL . Let the largest wavelength of a photon that can ionise this Hydrogen atom (with the electron now in an orbit with principal quantum number n − 1 ) be λM. Choose the correct option(s): (A) λL is proportional to (n(n−1)) 2 (2n−1) (B) ΔpL is proportional to 1 (n−1) 2 (C) ΔpL is proportional to (2n−1) (n(n−1)) 2 (D) λM is proportional to (n − 1) 2 Paragraph for Q. 31 - 33 A hydrogen like atom of atomic number Z is in excited state of quantum number 2n. It can emit a maximum energy photon of 204eV. If it makes transition to quantum state n, a photon of energy 40.8eV is emitted. Ground state energy of hydrogen atom is −13.6eV. 31. Find the value of n : (A) 3 (B) 2 (C) 4 (D) 6 32. Find ground state energy (in eV ) of this atom: (A) −187.6eV (B) −197.6eV (C) −217.6eV (D) −167.6eV 33. Calculate minimum energy (eV) that can be emitted by this atom during de-excitation: (A) 12.46 ev (B) 10.58eV (C) 11.97eV (D) 13.27eV Paragraph for Q. 34 - 35 A radioactive nucleus A decays into two different stable nuclei X and Y. The half-life for the decay of A into X is T1 and the half-life for the decay of A into Y is T2. 34. If at t = 0, there are N0 nuclei A present in a sample, the time instant when there are exactly N0 2 nuclei A present is: (A) 2T1T2 T1+T2 (B) T1T2 T1+T2 (C) T1 + T2 (D) T1+T2 2 35. If at t = 0, there were no nuclei X and Y present, the ratio of number of nuclei X to number of