A harmonic oscillator potential with natural frequency v contains a number of electrons

The electron in a hydrogen atom is somewhat like a particle confined to a three-dimensional box. In the atom, what plays the role of the confining box?

A friend who hasnt studied physics asks you the size of a hydrogen atom. How do you answer?

How many quantum numbers are required to specify fully the state of a hydrogen atom?

Both the Bohr and Schrdinger theories predict the same groundstate energy for hydrogen. Do they agree about the angular momentum in the ground state? Explain

Is it possible for a hydrogen atom to be in the 2d state? Explain

Can the component of a quantized angular momentum measured on a given axis ever equal the magnitude of the angular momentum vector? Explain.

The electron is a spin-1 2 particle. Does this mean the electrons intrinsic angular momentum is 1 2U? Explain.

How does the SternGerlach experiment provide convincing evidence for space quantization?

Why is there no spin-orbit splitting in hydrogens ground state?

How does the exclusion principle explain the diversity of chemical elements?

Helium and lithium exhibit very different chemical behavior, yet they differ by only one unit of nuclear charge. Explain

Why is stimulated emission essential for laser action?

What distinguishes a BoseEinstein condensate from ordinary matter?

Using physical constants accurate to four significant figures (see inside front cover), verify the numerical values of the Bohr radius a0 and the hydrogen ground-state energy E1.

A group of hydrogen atoms is in the same excited state, and photons with at least 1.5-eV energy are required to ionize these atoms. Whats the quantum number n for the initial excited state?

Find the maximum possible magnitude for the orbital angular momentum of an electron in the n = 7 state of hydrogen.

Which of the following is not a possible value for the magnitude of the orbital angular momentum in hydrogen: (a) 112 U; (b) 120 U; (c) 130 U; (d) 140 U; (e) 156 U?

The orbital angular momentum of the electron in a hydrogen atom has magnitude 2.585 *10-34 J# s. Find its minimum possible energy

Whats the orbital quantum number for an electron whose orbital angular momentum has magnitude L = 130 U?

A hydrogen atom is in the 6f state. Find (a) its energy and (b) the magnitude of its orbital angular momentum

Give a symbolic description for the state of the electron in a hydrogen atom with total energy -1.51 eV and orbital angular momentum 16 U.

Verify the value of the Bohr magneton mB in Equation 36.14.

Theories of quantum gravity predict a spin-2 particle called the graviton. What would be the magnitude of the gravitons spin angular momentum?

Some very short-lived particles known as delta resonances have spin 3 2. Find (a) the magnitude of their spin angular momentum and (b) the number of possible spin states.

What are the possible j values for a hydrogen atom in the 3D state?

An infinite square well contains nine electrons. Find the energy of the highest-energy electron in terms of the ground-state energy E1.

A quantum harmonic oscillator with frequency v contains 21 electrons. Whats the energy of the highest-energy electron?

Use shell notation to characterize rubidiums outermost electron.

Write the full electronic structure of scandium.

Write the full electronic structure of bromine.

Show that the wavelength l in nm of a photon with energy E in eV is l = 1240/E

The 4f S 3p transition in sodium produces a spectral line at 567.0 nm. Find the energy difference between these two levels.

The 4p S 3s transition in sodium produces a double spectral line at 330.237 nm and 330.298 nm. Whats the energy splitting of the 4p level?

Adapt part (b) of Example 36.1 to find the probability that an electron in the hydrogen ground state will be found beyond two Bohr radii.

Determine the principal and orbital quantum numbers for a hydrogen atom whose electron has energy 20.850 eV and orbital angular momentum L = 112U.

Find (a) the energy and (b) the magnitude of the orbital angular momentum for an electron in the 5d state of hydrogen.

Assuming the Moons orbital angular momentum is quantized, estimate its orbital quantum number l.

The maximum possible angular momentum for a hydrogen atom in a certain state is 30111U. Find (a) the principal quantum number and (b) the energy

A hydrogen atom is in an l = 2 state. What are the possible angles its orbital angular momentum vector can make with a given axis?

A hydrogen atom has energy E = -0.850 eV. Find the maximum possible values for (a) its orbital angular momentum and (b) the component of that angular momentum on a given axis.

An electron in hydrogen is in the 5f state. What possible values, in units of U, could a measurement of the orbital angular momentum component on a given axis yield?

Substitute Equation 36.3 into Equation 36.4 and carry out the differentiations to show that you get the first unnumbered equation following Equation 36.4.

Differentiate the radial probability density for the hydrogen ground state, and set the result to zero to show that the electron is most likely to be found at one Bohr radius.

Repeat Exercise 25 for the case where you know only that the principal quantum number is 3; that is, l might have any of its possible values.

A hydrogen atom is in the 4F5/2 state. Find (a) its energy in units of the ground-state energy, (b) its orbital angular momentum in units of U, and (c) the magnitude of its total angular momentum in units of U.

Suppose you put five electrons into an infinite square well of width L. Find an expression for the minimum energy of this system, consistent with the exclusion principle

A harmonic oscillator potential of natural frequency v contains eight electrons and is in its lowest-energy state. (a) What is its energy? (b) What would the lowest energy be if the electrons were replaced by spin-1 particles of the same mass?

You work for a nanotechnology company developing a new quantum device that operates essentially as a one-dimensional infinite square well of width 2.5 nm. Youre asked to specify the maximum number of electrons in the device before the total electron energy exceeds 25 eV. Your answer?

Determine the electronic configuration of copper

An electron in a highly excited state of hydrogen 1n1 W 12 drops into the state n = n2. Find the lowest value of n2 for which the emitted photon will be in the infrared.

A solid-state laser made from leadtin selenide has a lasing transition at a wavelength of 30 m. If its power output is 2.0 mW, how many lasing transitions occur each second?

For hydrogen, fine-structure splitting of the 2p state is only about 50 eV. What percentage is this difference of the photon energy emitted in the 2p S 1s transition? Your answer shows why its hard to observe spin-orbit splitting in hydrogen.

Find the probability that the electron in the hydrogen ground state will be found in the radial-distance range r = a0 { 0.1a0.

Youve acquired a laser for your dental practice. It produces 400-mJ pulses at 2.94@m wavelength. A patient wonders about the number of photons in each pulse, and where they lie in the EM spectrum. Your answer?

Singly ionized oxygen (so-called O-II) is a prevalent species in the tenuous gas between stars, and O-II emits a doublet spectral line at 372.60 nm and 372.88 nm. Astrophysicists analyze this line to learn, among other things, about the distribution of interstellar gas in distant galaxies. Find the energy splitting, in eV, that results in this doublet.

A harmonic oscillator potential with natural frequency v contains a number of electrons and is in its state of lowest energy. If that energy is 6.5Uv, (a) how many electrons are in the potential well and (b) whats the energy of the highest-energy electron?

A harmonic oscillator potential with natural frequency v contains N electrons and is in its state of lowest energy. Find expressions for the energy of the highest-energy electron for (a) N even and (b) N odd.

A harmonic oscillator potential with natural frequency v contains N electrons and is in its state of lowest energy. Find expressions for the total energy for (a) N even and (b) N odd.

lowest possible energy state, which is 19 times the ground-state energy E1 for the same well when it contains a single particle. (a) How many particles are in the well? (b) Whats the energy of the highest-energy particle?

Repeat Problem 58 for the case of an infinite square well containing N particles, rather than for a harmonic oscillator. Express your answer in terms of the ground-state energy E1.

Whats the most orbital angular momentum that could be added to an atomic electron initially in the 6d state without changing its principal quantum number? What would be the new state?

A hydrogen atom is in an F state. (a) Find the possible values for its total angular momentum. (b) For the state with the greatest angular momentum, find the number of possible values for the component of J S on a given axis.

A hydrogen atom is in the 2s state. Find the probability that its electron will be found (a) beyond one Bohr radius and (b) beyond 10 Bohr radii.

Show that the maximum number of electrons in an atoms nth shell is 2n2

Form the radial probability density P21r2 associated with the c2s state of Equation 36.7, and find the electrons most probable radial position.

Substitute the wave function c2 of Equation 36.7 into Equation 36.4 to verify that the equation is satisfied and that the energy is given by Equation 36.6 with n = 2.

(a) Verify Equation 36.8 by considering a single-electron atom with nuclear charge Ze instead of e. (b) Calculate the ionization energies for single-electron versions of helium, oxygen, lead, and uranium.

Excimer lasers for vision correction generally use a combination of argon and fluorine to form a molecular complex that can exist only in an excited state. Stimulated de-excitation produces 6.42-eV photons, which form the lasers intense beam. Whats the corresponding photon wavelength, and where in the spectrum does it lie?

A selection rule for the infinite square well allows only those transitions in which n changes by an odd number. Suppose an infinite square well of width 0.200 nm contains an electron in the n = 4 state. (a) Draw an energy-level diagram showing all allowed transitions that could occur as this electron drops toward the ground state, including transitions from lower levels that could be reached from n = 4. (b) Find all the possible photon energies emitted in these transitions.

An ensemble of one-electron square-well systems of width 1.17 nm all have their electrons in highly excited states. They undergo all possible transitions in dropping toward the ground state, obeying the selection rule that n must be odd. (a) What wavelengths of visible light are emitted? (b) Is there any infrared emission? If so, how many spectral lines lie in the infrared?

Use the radial probability density from Equation 36.5 and the normalized ground-state hydrogen wave function from Equation 36.3 and Example 36.1 to calculate the average radial distance rav for an electron in the ground state. (Note: Because the probability-density curve isnt symmetric, the average radial distance isnt the same as the most probable distance shown in Fig. 36.3.)

Follow the procedure in Problem 71 to calculate the average radial distance for an electron in the 2s state of hydrogen

The ratio of the magnetic moment, in units of the Bohr magneton mB, to the angular momentum, in units of U, is called the g-factor. (a) Show that the classical orbital g-factor for an atomic electron in a circular Bohr orbit is gL = 1. (b) Show that Equation 36.13 gives gS = 2 for the g-factor associated with electron spin

ou work for a company that makes red heliumneon lasers widely used in physics experiments. Figure 36.19 shows an energy-level diagram for this laser. An electric current excites helium to a metastable level E1 at 20.61 eV above the ground state. Collisions transfer energy to neon atoms, exciting them

Using the table below, make a plot of atomic volume versus atomic number, for the elements from Z = 30 to Z = 59 listed in the table. Comment on the structure of your graph in relation to the periodic table, the electronic structures of atoms, and their chemical properties. (Volumes are in units of 10-30 m3 .) Z V Z V Z V 30 7.99 40 26.1 50 11.2 31 12.5 41 20.2 51 8.78 32 6.54 42 18.8 52 6.88 33 4.99 43 17.5 53 5.28 34 3.71 44 16.2 54 4.19 35 2.85 45 12.8 55 95.9 36 2.57 46 12.0 56 51.6 37 70.3 47 11.2 57 49.0 38 37.2 48 10.5 58 46.5 39 28.3 49 17.2 59 44.0

Molybdenums X-ray spectrum has its Ka peak at 17.4 keV. The corresponding X-ray wavelength is closest to a. 1 pm. b. 100 pm. c. 1 nm. d. 100 nm

In general, how should the energy of an elements La X rays compare with the energy of its Ka X rays? a. They have less energy. b. They have the same energy. c. They have greater energy. d. You cant tell without knowing the element

Elements A and B have atomic numbers ZA and ZB = 2ZA. How do you expect element Bs Ka X-ray energy to compare with that of element A? a. Bs Ka energy should be about one-fourth that of A. b. Bs Ka energy should be about half that of A. c. Bs Ka energy should be about twice that of A. d. Bs Ka energy should be about four times that of A

Emission of characteristic X rays occurs in the context of multielectron atoms that generally have all but one of their electrons present. You should therefore expect the X-ray energies to be described a. quite accurately by Bohrs atomic theory. b. through hydrogen-like solutions to the Schrdinger equation. c. only approximately by Bohrs theory or hydrogenic solutions to the Schrdinger equation.