(a) Compute the oscillation frequency of the electron and the expected absorption or emission wavelength in a Thomson model hydrogen atom. Use R = 0.053 nm. Compare with the observed wavelength of the strongest emission and absorption line in hydrogen, 122 nm. (b) Repeat for sodium (Z = 11). Use R = 0.18 nm. Compare with the observed wavelength, 590 nm.

75.0 mL of 1.75 M HCl and 125.0 mL of 1.50 M NaOH are combined in constant-pressure calorimeter. Both solutions are initially at 23.9 °C. Calculate the final temperature of the combined solutions. (Use the data from Table 5.3. Assume that the mass of the combined solutions is 200.0 g and that the solution's specific heat is the same as that for water, $4.184\;\mathrm{J/g\cdot°C}$) The heat capacity of the calorimeter is negligibly small.

A 50.75-g sample of water at 75.6 °C is added to a sample of water at 24.1 °C in a constant-pressure calorimeter. If the final temperature of the combined water is 39.4 °C and the heat capacity of the calorimeter is 26.3 J/°C, calculate the mass of the water originally in the calorimeter.

A long time ago, in a galaxy far, far away, electric charge had not yet been invented, and atoms were held together by gravitational forces. Compute the Bohr radius and the n = 2 to n = 1 transition energy in a gravitationally bound hydrogen atom.

Draw an energy-level diagram showing the lowest four levels of singly ionized helium. Show all possible transitions from the levels and label each transition with its wavelength.