Draw an energy-level diagram, similar to Figure 38.21, for the He+ ion. On your diagram: Show all possible emission transitions from the n = 4 energy level.

A sample contains radioactive atoms of two types, A and B. Initially there are five times as many A atoms as there are B atoms. Two hours later, the numbers of the two atoms are equal. The half-life of A is 0.50 hour. What is the half-life of B?

The oxygen nucleus ¹⁶O has a radius of 3.0 fm. With what speed must a proton be fired toward an oxygen nucleus to have a turning point 1.0 fm from the surface? Assume the nucleus remains at rest.

At what speed is an electron’s de Broglie wavelength (a) 1.0 nm, (b) 1.0 μm, and (c) 1.0 mm?

The allowed energies of a simple atom are 0.00 eV, 4.00 eV, and 6.00 eV. Draw the atom’s energy-level diagram. Label each level with the energy and the quantum number.

An experiment has four possible outcomes, labeled A to D. The probability of A is P_A = 40% and of B is P_B = 30%. Outcome C is twice as probable as outcome D. What are the probabilities P_C and P_D?

A 1.0-mm-diameter sphere bounces back and forth between two walls at x = 0 mm and x = 100 mm. The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of speed. At a random instant of time, what is the probability that the center of the sphere is at exactly x = 50.0 mm?

A 1.0-mm-diameter sphere bounces back and forth between two walls at x = 0 mm and x = 100 mm. The collisions are perfectly elastic, and the sphere repeats this motion over and over with no loss of speed. At a random instant of time, what is the probability that the center of the sphere is between x = 49.0 mm and x = 51.0 mm?

An experiment finds electrons to be uniformly distributed over the interval 0 cm ≤ x ≤ 2 cm, with no electrons falling outside this interval. If 10⁶ electrons are detected, how many will be detected in the interval 0.79 to 0.81 cm?