BackA muon—a subatomic particle with charge −e and a mass 207 times that of an electron—is confined in a 15-pm-long, one-dimensional box. ( 1pm=1picometer=10−12 m.) What is the wavelength, in nm, of the photon emitted in a quantum jump from n = 2 to n = 1?
The first three energy levels of the fictitious element X are shown in FIGURE P38.54. What is the ionization energy of element X?
What wavelength photon does a hydrogen atom emit in a 200→199 transition?
What is the difference in the wavelengths emitted in a 199→2 transition and a 200→2 transition?
Consider a hydrogen atom in stationary state n. On average, an atom stays in the n = 2 state for 1.6 ns before undergoing a transition to the n = 1 state. On average, how many revolutions does the electron make before the transition?
Draw an energy-level diagram, similar to Figure 38.21, for the He+ ion. On your diagram: Show the ionization limit.
Very large, hot stars—much hotter than our sun—can be identified by the way in which He+ ions in their atmosphere absorb light. What are the three longest wavelengths, in nm, in the Balmer series of He+?
INT A beam of electrons is incident upon a gas of hydrogen atoms. What minimum speed must the electrons have to cause the emission of 656 nm light from the 3→2 transition of hydrogen?
FIGURE EX39.14 is a graph of |ψ(x)|2 for an electron. What is the value of a?
FIGURE P39.31 shows the wave function of a particle confined between x = 0 nm and x = 1.0 nm. The wave function is zero outside this region. Draw a graph of the probability density P(x)=|ψ(x)|2
FIGURE P39.31 shows the wave function of a particle confined between x = 0 nm and x = 1.0 nm. The wave function is zero outside this region. Calculate the probability of finding the particle in the interval 0 nm ≤ x ≤ 0.25 nm.
Consider the electron wave function where x is in cm. Determine the normalization constant c.
Consider the electron wave function where x is in cm. Draw a graph of ψ(x) over the interval −2 cm ≤ x ≤ 2 cm. Provide numerical scales on both axes.
Consider the electron wave function where x is in cm. Draw a graph of |ψ(x)|2 over the interval −2 cm ≤ x ≤ 2 cm. Provide numerical scales.
A particle is described by the wave function where L = 2.0 mm. Sketch graphs of both the wave function and the probability density as functions of x.