Physics 215 Winter 2002 Introduction to Modern Physics Prof. Ioan Kosztin Homework #3 1. (Q3/p137) Can the electron in the ground state of the hydrogen atom absorb a photon of energy (a) less than 13.6 eV and (b) greater than 13.6 eV? [5 pt] 2. (Q4/p137) Explain the concept of an atomic stationary state. Why is this idea of central importance in explaining the stability of the Bohr atom? [5 pt] 3. (Q8/p137) What factor causes the finite width of the peaks in the I-V curve of the Franck-Hertz experiment? [5 pt] 4. (Q4/p180) If matter has a wave nature, why is this wave-like character not observable in our daily experiences? [5 pt] 5. (P3/p137) A mystery particle enters the region between the plates of a Thomson apparatus as shown in Figure 3.5. The deflection angle θ is measured to be 0.20 radians (downwards) for this particle when V= 2000 V, ℓ = 10.0 cm, and d = 2.00 cm. If a perpendicular magnetic field of magnitude 4.57 X 10-2 T is applied simultaneously with the electric field, the particle passes through the plates without deflection. (a) Find q/m for this particle. (b) Identify the particle. (c) Find the horizontal speed with which the particle entered the plates. (d) Must we use relativistic mechanics for this particle? [5 pt] Figure 3.5 Deflection of negative particles by an electric field.Physics 215 Homework #3 - 2 - 6. (P5/p138) A Thomson type experiment with relativistic electrons: One of the earliest experiments to show that p = γmv (rather than p = mv) was that of Neumann. [G. Neumann, Ann. Physik, 45:529 (1914)]. The apparatus shown in Figure P3.5 is identical to Thomson's except that the source of high-speed electrons is a radioactive radium source, and the magnetic field B is arranged to act on the electron over its entire trajectory from source to detector. The combined electric and magnetic fields act as a velocity selector, only passing electrons with speed r, where v = V/Bd (Equation 3.6), while in the region where there is only a magnetic field the electron moves in a circle of radius r, with r given by p = Bre. This latter region (E = 0, B = constant) acts as a momentum selector because electrons with larger momenta have paths with larger radii. (a) Show that the radius of the circle described by the electron is given by r = (ℓ2 + y2)/2y. (b) Typical values for the Neumann experiment d = 2.51 X 10-4 m, B = 0.0177 T, and ℓ = 0.0247 m. For V= 1060 volts, y, the most critical value, was measured to be 0.0024 ± 0.0005 m. Show that these values disagree with the y value calculated from p=mv but agree with the y value calculated from p = γmv within experimental error. (Hint: Find r from Equation 3.6, use mv = Bre or γmv = Bre to find r, and use r to find y.) [5 pt] Center of curvature Figure P3.5 The Neumann apparatus. 7. (P6/p138) In a Millikan oil drop experiment, the condenser plates are spaced 2.00 cm apart, the potential across the plan is 4000 V, the rise or fall distance is 4.00 mm, the density of the oil droplets is 0.800 g/cm3, and the viscosity of the air is 1.81 X 10-5 kg·m-ls-1. The avenge time of fall in the absence of an electric field is 15.9 s. The following different rise times in seconds are served when the field is turned on: 36.0, 17.3, 24.0, 11.4, 7.54. (a) Find the radius and mass of the drop used in this experiment, (b) Calculate the cha on each drop, and show that charge is quantized by considering both the size of each charge and the amount of charge gained (lost) when the rise time changes, (c)Physics 215 Homework #3 - 3 - Determine the electronic charge from these data. You may assume that e lies between 1.5 and 2.0 X 10-19 C. [5 pt] 8. (P29/p140) An electron initially in the n=3 state of a one-electron atom of mass M at rest undergoes a transition to the n=1 ground state. (a) Show that the recoil speed of the atom from emission of a photon is given approximately by v=8hR/9M. (b) Calculate the percent of the 3->1 transition energy that is carried off by the recoiling atom if the atom is deuterium. [5 pt] 9. (P25/p182) A woman on a ladder drops small pellets toward a spot on the floor. (a) Show that, according to the uncertainty principle, the miss distance must be at least 4/12/1)2/()2/( gHmx ==∆, where H is the initial height of each pellet above the floor and m is the mass of each pellet. (b) If H=2.0 m and m=0.50 g, what is ∆x ? [5 pt] 10. (P29/p183) An excited nucleus with a lifetime of 0.100 ns emits a γ-ray of energy 2.00 MeV. Can the energy width (uncertainty in energy, ∆E) of this 2.00-MeV γ emission line be directly measured if the best gamma detectors can measure energies to ±5 eV ? [5 pt] The homework is due in class on Mar. 14,