Exercise 1 Atomic line spectra 1/9

Transcription

1 Exercise 1 Atomic line spectra 1/9 The energy-level scheme for the hypothetical one-electron element Juliettium is shown in the figure on the left. The potential energy is taken to be zero for an electron at an infinite distance from the nucleus (when the electron is therefore not bound to the nucleus). 1. How much energy (in ev) does it take to ionize an electron from the ground level? An 18-eV photon is absorbed by a Juliettium atom in its ground level. 2. As the atom returns to its ground level, what possible energies can the emitted photons have? Assume that there can be transitions between all pairs of levels. [Hint: it helps to draw a sketch to determine all the possible transitions.] 3. What will happen if a photon with an energy of 8eV strikes a Juliettium atom in its ground level? Why? 4. Photons emitted in the Juliettium transitions n=3 à n=2 and n=3 à n=1 will eject photoelectrons from an unknown metal, but the photon emitted from the transition n=4àn=3 will not. What are the lower and upper limits one can deduce for the work function of the metal?

2 Exercise 1 Atomic line spectra 2/9

3 Exercise 2 X-ray spectra 3/9 Determine the correct equation to describe the K b frequencies measured by Moseley. The K b line of a certain element has a wavelength of 0.131nm. What is the element? [Hint: use the class notes, including the extra documents, published on the web to deduce the expression of f Kb ].

4 Exercise 3 X-ray scattering 4/9 X-ray of wavelength l = 0.186nm are scattered from NaCl [interatomic distance d = 0.282nm]. What is the angular separation between first- and second-order diffraction peaks? Assume scattering planes that are parallel to the surface.

5 Exercise 4 De Broglie wavelength 5/9 What is the De Broglie wavelength of the 1.0-TeV (1TeV=10 12 ev) protons (total energy) accelerated at the Fermilab Tevatron accelerator? These high-energy protons are needed to probe elementary particles [Hint: You need to use relativistic formula, rest mass energy of the proton: m p c 2 = MeV].

6 Exercise 5 De Broglie wavelength / uncertainty principle 6/9 We want to probe the location of a particle, e.g. an electron, to within 5x10-12 m using electromagnetic waves. 1. How small must the wavelength of the electromagnetic waves be? 2. Calculate the momentum and energy of a photon with such a wavelength. 3. If the particle is an electron with Dx = 5x10-12 m, what is the corresponding uncertainty in its momentum? [Note: results can be given either in SI or in Microscopic units.]

7 Exercise 6 Neutron scattering 7/9 A beam of thermal neutrons emerges from a nuclear reactor and is incident on a crystal as shown in the figure. The beam is Bragg scattered from the crystal whose scattering planes are separated by d=0.247nm. From the continuous energy spectrum of the beam, we wish to select neutrons of kinetic energy K=0.0105eV [non-relativistic energy]. 1. Find the Bragg scattering angle that results in a scattered beam of this energy. [Rest mass energy of the neutron: m n c 2 =939.6 MeV] 2. Will other energies also be present in the scattered beam? Explain.

8 Exercise 6 Neutron scattering 8/9

9 Exercise 7 Uncertainty principle 9/9 A mass of 1µg has a speed v=1cm/s. If its speed is uncertain by Dv/v=0.01(or 1%), what is the order of magnitude of the minimum uncertainty in its position? Do you think you could measure this position uncertainty? [Caution: watch the units!]