Modern Physics-02-OBJECTIVE SOLVED

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. Ans. (c) Solution: The gain in K.E. of a charged particle after moving through a potential difference of V is given by eV, that is also equal to where is the velocity of the charged particle. Disregarding the relativistic effect, de Broglie wavelength Putting . Problem 4. There are two radioactive substances and . Decay constant of is two times that of . Initially, both have equal number of nuclei. After half lives of , rate of disintegration of both are equal. The value of is (a) 4 (b) 2 (c) 1 (d) 5. Ans. (c) Solution: Let If is total no. of atoms in and at , then initial rate of disintegration of , and initial rate of disintegration of As i.e. half life of is half the half life of . After one half life of Equivalently, after two half lives of Clearly, , after , i.e., one half life of . Problem 5. A hydrogen atom is in an excited state of principal quantum number ( ) it emits a photon of wavelength ( ), when it returns to the ground state. The value of is (a) (b) (c) (d) . Ans. (d) Solution: As Multiply both sides by or . Problem 6. The weight based ratio of and in a sample of rock is 4 : 3 . If the half life of is years, then the age of rock is (a) years (b) years (c) years (d) years. Ans. (d) Solution: Let initial no. of U-atoms = After time , (age of rock), let no. of atoms remaining undecayed . = years. Problem 7. Binding energy per nucleon vs mass number curve for nuclei is shown in the figure. W, X, Y and Z are four nuclei indicated on the curve. The process that would release energy is (a) Y 2Z (b) W X + Z (c) W 2Y (d) X Y + Z. Ans. (c) Solution: If it mass Reactant: MeV Product: MeV MeV ENDOTHERMIC If it was MeV MeV MeV ENDOTHERMIC If it was MeV MeV Mev EXOTHERMIC If it was MeV MeV MeV ENDOTHERMIC Problem 8. In the sun about 4 billion kg of matter is converted to energy each second. The power output of the sun in watt is (a) (b) (c) (d) . Ans. (b) Solution: kgs-1 Js-1 . Problem 9. A star initially has deutrons. It produces energy via the processes and . If the average power radiated by the star is , the deuteron supply of the star is exhausted in a time of the order of (a) (b) (c) (d) . (The masses of nuclei are: , ) Ans. (c) Solution: MeV As each reaction involves 3 deuterons, so total number of reactions involved in the process . If each reaction produces an energy , then Time of exhaustion of the star . Problem 10. Consider the following reaction . If ; . The energy released (in MeV) in this fusion reaction is (a) 12 (b) 6 (c) 24 (d) 48. Ans. (c) Solution: Since, MeV MeV.