Quantum Physics Numericals PDF

Unit I: Quantum Physics 1. Find the de Broglie wavelength of (a) an electron with speed 1 * 10 8 m/s & 2 * 108 m/s (b) 40 keV electron used in a microscope (c) 1 mg grain of sand blown by the wind at a speed of 20 m/s. 2. Find the kinetic energy of an electron whose de Broglie wavelength...

Unit I: Quantum Physics 1. Find the de Broglie wavelength of (a) an electron with speed 1 * 10 8 m/s & 2 * 108 m/s (b) 40 keV electron used in a microscope (c) 1 mg grain of sand blown by the wind at a speed of 20 m/s. 2. Find the kinetic energy of an electron whose de Broglie wavelength is the same as that of a 100 keV x-ray. 3. The position and momentum of a 1 keV electron are simultaneously determined. If its position is located to within 0.1 nm, what is the percentage of uncertainty in its momentum? 4. An electron is in a box 0.1 nm across, which is the order of magnitude of atomic dimensions. Find its permitted energies. 5. An electron is confined in an infinite potential well of length L = 10 -10 m. Calculate the zero point energy of the electron. 6. Calculate the uncertainty in wavelength of a light emitted when an atom undergoes transition from an excited state that lasts for 10 -3 second. 16 7. In a Compton experiment, the frequency of an incident photon is 5 * 10 Hz. Calculate the de Broglie wavelength of the scattered electron when the scattering angle of the photon is (a) 90° and (b) 180°. 8. A particle is known to be in the ground state of an infinite square well with length L. Calculate the probability that the particle will be found in the middle half of the well, that is, between x = L/4 and x = 3L/4. 9. A small object of mass 1 mg is confined to move between two rigid walls separated by 2 cm. (a) Calculate the minimum speed of the object. (b) If the speed of the object is 4 cm/s, find the corresponding value of ‘n’. 10. An x-ray photon of initial frequency 3 * 1019 Hz collides with an electron and is scattered through 90°. Find its new frequency. 11. A particle moving with kinetic energy equal to its rest mass energy has a de Broglie wavelength of 1.78 * 10 -6 Å. If the kinetic energy doubles, what is the new de Broglie wavelength? 12. The speed of the bullet (m = 50g) and the speed of an electron ( m = 9.1 * 10 -28g) are measured to be the same, namely 300 m/s, with an uncertainty of 0.01%. With what fundamental accuracy could we have located the position of each, if the position is measured simultaneously with the speed in the same expt.? 13. Calculate the uncertainty ΔE in the energy of the excited state of an atom. (Given lifetime of excited state = 10-8 s) 14. Show that if the uncertainty in the location of a particle is about equal to its de Broglie wavelength, then the uncertainty in its velocity is about equal to one tenth its velocity. 15. An electron and a photon each have a wavelength of 2 Å. What are their momenta and total energies? 16. An electron is confined to a 1-D box of length L. When the electron makes a transition from its first excited state to the ground state, it emits a photon of energy 0.20eV. (a) What is the ground state energy in eV of the electron in the box? (b) Sketch the wave function of the electron in the third excited state. (c) If the boxes were made longer, how would the electrons new energy level spacing compare with its old ones? Would they be greater, smaller or same? 17. Suppose that an STM scans a surface at a distance of a=1 nm. Take the height of the potential energy barrier to be U0-E = 2 eV. If the distance between the surface and the STM tip decreases by 0.010nm, estimate the percentage of change in the tunneling current. 18. A Photon of energy 240 KeV is scattered by a free electron. If the recoil electron has a Kinetic energy of 190 KeV, what is the wavelength of the scattered photon? 19. What is the probability of electron to emerge on the other side of the barrier? (b) How different it would be if the barrier is twice the wide? 20. Electrons with energies of 0.4 eV are incident on a barrier 3 eV high and 0.1 nm wide. Find the approximate probability for the electrons to penetrate the barrier. 21. A beam of electrons is incident on a barrier 6 eV high and 0.2 nm wide. Find the energy they should have if 1% of them are to get through the barrier. 22. The wave function of a certain particle is ψ = A cos2x for - π /2 < x < π /2. (i) Find the value of A. (ii) Find the probability that the particle be found between x = 0 and x = π/4. 23. At a given temperature, λmax = 6500 Å for a blackbody cavity. What will λmax be if the  temperature of the cavity walls is increased so that the rate of emission of spectral radiation is doubled? 24. Through what angle must a 0.2 MeV photon be scattered by a free electron so that it loses 10% of its energy? 25. If Δλ/λ = 10-7 for a photon, what is the simultaneous value for Δx for λ = 5 Å and 5000 Å.