The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed.

The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (b) Calculate the wavelengths of the first three lines in the Lyman series—those for which ni = 2, 3, and 4.

One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. a. In what region of the electromagnetic spectrum is this emission found?

One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. b. Determine the initial and final values of n associated with this emission.

The hydrogen atom can absorb light of wavelength 1094 nm. (b) Determine the final value of n associated with this absorption.

Order the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n = 3 to n = 6, n = 4 to n = 9, n = 2 to n = 3, and n = 1 to n = 2.

Use the de Broglie relationship to determine the wavelengths of the following objects: (a) an 85-kg person skiing at 50 km/hr (b) a 10.0-g bullet fired at 250 m/s

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.

Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of 1.25 Å. The mass of a neutron is 1.675×10−27 kg.

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 (5.00±0.01) × 104 m/s. The mass of a proton is 1.673×10−27 kg.

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 b. n = 4?

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 2p subshell

A certain orbital of the hydrogen atom has n = 4 and l = 2. a. What are the possible values of ml for this orbital?

A certain orbital of the hydrogen atom has n = 4 and l = 2. 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}.

(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?

(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?

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?