Tiêu đề QM DPP Sheet 05 (1).pdf ✅

1 North Delhi : 56-58, First Floor, Mall Road, G.T.B. Nagar (Near Metro Gate No. 3), Delhi-09, Ph: 011-41420035 South Delhi : 28-A/11, Jia Sarai, Near-IIT Metro Station, New Delhi-16, Ph : 011-26851008, 26861009 IIT JAM PHYSICS 2024 (Online Batch) Section: MODERN PHYSICS (Quantum Mechanics) Chapter: UNCERTAINTY PRINCIPLE Daily Practice Problem (DPP) Sheet 5 PART I: Multiple Choice Questions (MCQ) 1. Assume that the uncertainty in the location of the particle A is equal to its de-broglie wavelength. The minimum uncertainty in the measurement of velocity ‘v’ of the particle is (a) 2 v  (b) 4 v  (c) v  (d) 8 v  2. If x is the uncertainty in location of the wave and  the simultaneous uncertainty in wavelength, then the uncertainty relation can be written as (a) 2 4 x      (b) 4 h x      (c) 4 h  x   (d) 1 4  x   3. A hydrogen atom is 5.3×10–11 m in radius. The minimum uncertainty in the momentum of an electron in this atom can have (a) 9.9×10–25 kg m/s (b) 9.9×10–28 kg m/s (c) 1×10–25 kg m/s (d) 2×10–25 kg m/s 4. A free 10 eV electron moves along x-direction with a speed 0.01c which can be measured with a precision of 1%. The uncertainty in the position of the particle will be \ (a) 1.12 nm (b) 3.86 nm (c) 4.58 nm (d) 6.74 nm 5. The average time that the atomic system remains in a energy state whose spectral line width is 10-4 A0 for 0   4000A , is (a) 1.24 ns (b) 2.78 ns (c) 6.28 ns (d) 8.48 ns PART II: Numerical Answer Type (NAT) Questions 6. A proton is confined to nucleus of radius 5 fm. The minimum value of kinetic energy of proton is ____________________________________________________________________________ KeV [Your answer should be AN INTEGER] 7. Consider an electron and proton is confined within a 10 fm box. Ratio of uncertainities of their velocities is _________________________________________ [Assume that, both are moving with same velocity] [Your answer should be AN INTEGER]