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ANSWERS OBJECTIVE UNSOLVED LEVEL – I 1. (d) 2. (d) 3. (c) 4. (d) 5. (d) 6. (a), (b), (c), (d) 7. (b) 8. (d) 9. (d) 10. (c) 11. (d) 12. (d) 13. (a) 14. (c) 15. (b) OBJECTIVE UNSOLVED LEVEL – II 1. (d) 2. (b) 3. (a) 4. (c) 5. (a) 6. (b) 7. (a) 8. (c) 9. (a) 10. (d) 11. (a) 12. (b) 13. (d) 14. (b) 15. (c) SUBJECTIVE UNSOLVED (C.B.S.E.) LEVEL – I 1. 6572 Å, 4870 Å, 4348Å, 4109Å. 2. MeV MeV 3. m 4. (i) 1225Å (ii) 48 eV (ii) 122 V . 5. 0.27Å 6. (a) + 3.4 eV (b) –6.8 eV (c) (b) is change (d) 1217 Å. 7. (a) 27.6 keV (b) of the order of 30 kV 8. 9. Q MeV 10. MeV MeV. SUBJECTIVE UNSOLVED LEVEL – II 1. 2. 123, 2.86 and 0.186 pm 3. 0.45 KeV 4. 39.2 MeV, 5.6 MeV 5. 2.21 MeV 6. (a) (b) kg/day (c) 1264 kg 7. (a) (b) 0.028 min-1(Approx) (c) 25 min (approx) 8. (a) (b) 64 min. 9. 1800y 10. 11. (a) (b) (c) 0.248 Å 12. 13. (i) 3.4 eV (ii) Å

PROBLEMS 1. The element curium Cm has a mean life of seconds. Its primary decay modes are spontaneous fission and decay, the former with a probability of 8% and the latter with a probability of 92%. Each fission release 200 MeV of energy. The masses involved in decay are as follows : Calculate the power output form a sample of Cm atoms. (1u = 931meV/c2). 2. Nuclei of a radioactive element A are being produced at a constant rate . The element has decay constant . At time t = 0, there are N0 nuclei of the element. (a) Calculate the number N of nuclei of A at time t. (b) If , calculate the number of nuclei of A after one half life of A and also the limiting value of N as t . 3. (a) A hydrogen like atom of atomic number Z is in an excited state of quantum number 2n. It can emit a maximum energy photon of 204 eV. If it makes a transition to quantum state n, a photon of energy 40.8 eV is emitted. Find n, Z and the ground state energy (in eV) of this atom. Also calcula

SUBJECTIVE UNSOLVED LEVEL - II (BRUSH UP YOUR CONCEPTS) 1. Find the binding energy of an electron in the ground state of hydrogen-like ions in whose spectrum the third line of the Balmer series is equal to 108.5 nm. 2. Calculate the de Broglie wavelengths of an electron, proton, and uranium atom, all having the same kinetic energy 100 eV. 3. What amount of energy should be added to an electron to reduce its de Broglie wavelength from 100 to 50 pm? 4. Find the binding energy of the nucleus of lithium isotope and hence find the binding energy per nucleon in it. Given atom amu; atom = 1.007825 amu; amu. 5. A neutron with kinetic energy MeV activates a nuclear reaction whose threshold MeV. Find the kinetic energy of the alpha particles outgoing at right angles to the incoming neutron’s direction. [Take 1 amu MeV] 6. A town has a population of 1 million. The average electric power needed per person is 300 W. A reactor is to be designed to supply power to this town. The

SUBJECTIVE UNSOLVED (C.B.S.E.) LEVEL – I (REVIEW YOUR CONCEPTS) 1. Using the Rydberg formula, calculate the wavelength of the first four spectral lines in the Balmer series of the hydrogen spectrum. 2. Find the energies in units of for the ground state and the first excited state for an electron confined to a line of length m and also find the energies in units of for the ground state and the first excited states of a neutron confined to a line of length m. 3. A beam of 35.0 keV electrons strikes a molybdenum (42 M096 target. What is the cut-off wavelength of the X-rays generated? 4. Using Bohr’s formula for energy quantization, determine (i) the longest wavelength in the Lyman series of hydrogen atom spectrum. (ii) the excitation energy of the level of atom. (iii) the ionization potential of the ground state of atom. 5. The wavelength of the line emitted by hydrogen-like element is 0.32Å. Determine the wavelength of the line emitted by the same element. 6.

OBJECTIVE UNSOLVED LEVEL - I 1. In which of the following transitions will the wavelength be minimum? (a) to (b) to (c) to (d) to . 2. In which of the following systems will the radius of the first orbit be a minimum? (a) hydrogen atom (b) deuterium atom (c) singly ionized helium (d) doubly ionized lithium. 3. Which of the following curves may represent the speed of the electron in a hydrogen atom as a function of the principal quantum number ? 4. Which of the following parameters are the same for all hydrogen-like atoms and ions in their ground states? (a) radius of the orbit (b) speed of the electron (c) energy of atom (d) orbital angular momentum of the electron. 5. Frequencies of X-rays of different materials are measured. Which one of the graphs in figure may represent the relation between the frequency and the atomic number ? 6. X-rays incident on a material (a) exerts a force on it (b) transfers energy to it (c) transfers momen

SOLVED SUBJECTIVE PROBLEMS Problem 1. How may different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are excited to states with principal quantum number ? Solution: From the th state, the atom may go to th state, …., 2nd state or 1st state. So there are th possible transitions staring from the th sate. The atoms reaching th state may make different transitions. Similarly for other lower states. The total number of possible transitions is . Problem 2. A doubly ionized lithium atom is hydrogen-like with atomic number Z = 3. Find the wavelength of the radiation required to excite the electron in from the first to the third Bohr orbit. Given the ionization energy of hydrogen atom as 13.6 eV. Solution: The energy of orbit of a hydrogen-like atom is given as Thus for atom, as Z = 3, the electron energies for the first and third Bohr orbits are : For n = 1, For n = 3, Thus the energy required to transfer an

SOLVED OBJECTIVE PROBLEMS Problem 1. The ratio of minimum to maximum wavelengths of radiation that an excited electron in a hydrogen atom can emit while going to the ground state is (a) 1/2 (b) Zero (c) 3/4 (d) 27/32. Ans. (c) Solution: Energy of radiation that corresponds to the energy difference between two energy levels and is given as is minimum when & is maximum when & (the atom is ionized, that is known as ionization energy) . Problem 2. The wavelength of X-ray produced by an X-ray tube is 0.76 Å. The atomic number of anticathode material is (a) 82 (b) 41 (c) 20 (d) 10. Ans. (b) Solution: For X-ray line, …(i) With reference to given data, Å = 0.76 m m Putting these values in equation (i) . Problem 3. If the stationary proton and - particle are accelerated through same potential difference, the ratio of de Broglie’s wavelength will be (a) 2 (b) 1 (c) (d) none of these.

MODERN PHYSICS WAVE PARTICLE DUALITY: Despite their wave nature, electromagnetic radiations, have properties akin to those of particles. Electromagnetic radiation is an emission with a dual nature, i.e. it has both wave and particle aspects. In particular, the energy conveyed by an electromagnetic wave is always carried in packets whose magnitude is proportional to frequency of the wave. These packets of energy are called photons. Energy of photon is h. , where is Planck’s constant, and is frequency of wave. According to de-Broglie As wave behaves like material particles, similarly matter also behaves like waves. According to him, a wavelength of the matter wave associated with a particle is given by , where is the mass and v is velocity of the particle. If an electron id accelerated through a potential difference of V volt, then or (It is assumed that the voltage V is not more than several tens of Kilovolt) Brain Teaser: 1. Why is the wave nature of ma

UNSOLVED OBJECTIVE LEVEL – I 1. In a simple harmonic motion (a) the potential energy is always equal to the kinetic energy (b) the potential energy is never equal to the kinetic energy (c) the average potential energy in any time interval is equal to the average kinetic energy in that time interval (d) the average potential energy in one time period is equal to the average kinetic energy in this period. 2. For a simple pendulum the graph between and will be : (a) hyperbola (b) parabola (c) a curved line (d) a straight line. 3. The time period of a particle in simple harmonic motion is equal to the time between consecutive appearances of the particle at a particular point in its motion. This point is (a) the mean position (b) an extreme position (c) between the mean position and the positive extreme (d) between the mean position and the negative extreme. 4. A pendulum clock keeping correct time is taken to high altitudes, (a) it will keep correct time

SIMPLE HARMONIC MOTION PERIODIC MOTION: Periodic motion of a body is that motion which is repeated identically after a fixed interval of time. Examples (i) The revolution of earth around the sun is a periodic motion. Its period of revolution is one year. (ii) The motion of hands of a clock is a periodic motion. The period of motion of hour’s hand of a clock is 12 hours, of minute’s hand of a clock is 1 hour and of second’s hand of a clock is one minute. (iii) Uniform circular motion is a periodic motion. OSCILLATORY MOTION: Oscillatory or Vibratory motion is that motion in which a body moves to and fro or back and forth repeatedly about a fixed point (called mean position), in a definite interval of time. In such a motion, the body is confined within well defined limits (called extreme positions) on either side of mean position. Thus a periodic and bounded motion of a body about a fixed point is called an oscillatory or vibratory motion. (i) The motion of the bob of a