Use the de Broglie relationship to determine the wavelengths of the following objects: (c) a lithium atom moving at 2.5 × 10⁵ m/s (d) an ozone (O₃) molecule in the upper atmosphere moving at 550 m/s.

Among the elementary subatomic particles of physics is the muon, which decays within a few microseconds after formation. The muon has a rest mass 206.8 times that of an electron. Calculate the de Broglie wavelength associated with a muon traveling at 8.85 * 105 cm/s.

Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of (a) a 1.50-mg mosquito moving at a speed of 1.40 m/s if the speed is known to within {0.01 m/s;

Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of (b) a proton moving at a speed of 15.00 { 0.012 * 104 m/s. (The mass of a proton is given in the table of fundamental constants in the inside cover of the text.)

Calculate the uncertainty in the position of (a) an electron moving at a speed of 13.00 ± 0.012 × 10⁵ m/s (b) a neutron moving at this same speed. (The masses of an electron and a neutron are given in the table of fundamental constants in the inside cover of the text.)

(a) For n = 4, what are the possible values of l?

How many unique combinations of the quantum numbers l and ml are there when (a) n = 1 (b) n = 5?

Give the numerical values of n and l corresponding to each of the following orbital designations: (a) 3p (b) 2s (c) 4f

Give the numerical values of n and l corresponding to each of the following orbital designations: (d) 5d.

Give the values for n, l, and ml for (a) each orbital in the 3p subshell, (b) each orbital in the 4f subshell.

A certain orbital of the hydrogen atom has n = 4 and l = 3. (a) What are the possible values of ml for this orbital?

A certain orbital of the hydrogen atom has n = 4 and l = 3. (b) What are the possible values of ms for the orbital?

Which of the following represent impossible combinations of n and l? (a) 1p (b) 4s (c) 5f (d) 2d

For the table that follows, write which orbital goes with the quantum numbers. Don't worry about x, y, z subscripts. If the quantum numbers are not allowed, write 'not allowed.' n l ml Orbital 2 1 -1 2p (example) 1 0 0 3 -3 2 3 2 -2 2 0 -1 0 0 0 4 2 1 5 3 0

Sketch the shape and orientation of the following types of orbitals: (a) s, (b) p_z, (c) d_xy.

Sketch the shape and orientation of the following types of orbitals: (a) p_x, (b) d_z2, (c) d_{x2 - y2}.

(c) What can you say about the average distance from the nucleus of an electron in a 2s orbital as compared with a 3s orbital?

(d) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): 4f, 6s, 3d, 1s, 2p.

(a) With reference to Figure 6.19, what is the relationship between the number of nodes in an s orbital and the value of the principal quantum number?

(b) Identify the number of nodes; that is, identify places where the electron density is zero, in the 2px orbital; in the 3s orbital.

(d) For the hydrogen atom, list the following orbitals in order of increasing energy: 3s, 2s, 2p, 5s, 4d.

(a) For an He+ ion, do the 2s and 2p orbitals have the same energy? If not, which orbital has a lower energy?

(b) If we add one electron to form the He atom, would your answer to part (a) change?

(a) The average distance from the nucleus of a 3s electron in a chlorine atom is smaller than that for a 3p electron. In light of this fact, which orbital is higher in energy?

(b) Would you expect it to require more or less energy to remove a 3s electron from the chlorine atom, as compared with a 2p electron?

Two possible electron configurations for an Li atom are shown here. (c) In the absence of an external magnetic field, can we say that one electron configuration has a lower energy than the other? If so, which one has the lowest energy?

An experiment called the Stern–Gerlach experiment helped establish the existence of electron spin. In this experiment, a beam of silver atoms is passed through a magnetic field, which deflects half of the silver atoms in one direction and half in the opposite direction. The separation between the two beams increases as the strength of the magnetic field increases. (a) What is the electron configuration for a silver atom?

An experiment called the Stern–Gerlach experiment helped establish the existence of electron spin. In this experiment, a beam of silver atoms is passed through a magnetic field, which deflects half of the silver atoms in one direction and half in the opposite direction. The separation between the two beams increases as the strength of the magnetic field increases. (c) Would this experiment work for a beam of fluorine (F) atoms?