Answer: How do the allowed orbits for electrons in atoms differ from the allowed orbits

Name three different types of evidence for the existence of atoms.

Explain why patterns observed in the periodic table of the elements are evidence for the existence of atoms, and why Brownian motion is a more direct type of evidence for their existence.

If atoms exist, why cant we see them with visible light?

What two pieces of evidence allowed the first calculation of me , the mass of the electron? (a) The ratios qe / me and q p / m p . (b) The values of qe and EB . (c) The ratio qe / me and qe . Justify your response.

How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.

How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.

Explain how Bohrs rule for the quantization of electron orbital angular momentum differs from the actual rule.

What is a hydrogen-like atom, and how are the energies and radii of its electron orbits related to those in hydrogen?

Explain why characteristic x rays are the most energetic in the EM emission spectrum of a given element.

Why does the energy of characteristic x rays become increasingly greater for heavier atoms?

Observers at a safe distance from an atmospheric test of a nuclear bomb feel its heat but receive none of its copious x rays. Why is air opaque to x rays but transparent to infrared?

Lasers are used to burn and read CDs. Explain why a laser that emits blue light would be capable of burning and reading more information than one that emits infrared.

Crystal lattices can be examined with x rays but not UV. Why?

CT scanners do not detect details smaller than about 0.5 mm. Is this limitation due to the wavelength of x rays? Explain.

How do the allowed orbits for electrons in atoms differ from the allowed orbits for planets around the sun? Explain how the correspondence principle applies here.

Atomic and molecular spectra are discrete. What does discrete mean, and how are discrete spectra related to the quantization of energy and electron orbits in atoms and molecules?

Hydrogen gas can only absorb EM radiation that has an energy corresponding to a transition in the atom, just as it can only emit these discrete energies. When a spectrum is taken of the solar corona, in which a broad range of EM wavelengths are passed through very hot hydrogen gas, the absorption spectrum shows all the features of the emission spectrum. But when such EM radiation passes through room-temperature hydrogen gas, only the Lyman series is absorbed. Explain the difference.

Lasers are used to burn and read CDs. Explain why a laser that emits blue light would be capable of burning and reading more information than one that emits infrared.

The coating on the inside of fluorescent light tubes absorbs ultraviolet light and subsequently emits visible light. An inventor claims that he is able to do the reverse process. Is the inventors claim possible?

What is the difference between fluorescence and phosphorescence?

How can you tell that a hologram is a true three-dimensional image and that those in 3-D movies are not?

How is the de Broglie wavelength of electrons related to the quantization of their orbits in atoms and molecules?

What is the Zeeman effect, and what type of quantization was discovered because of this effect?

Define the quantum numbers n, l, ml , s , and ms .

For a given value of n , what are the allowed values of l ?

For a given value of l , what are the allowed values of ml ? What are the allowed values of ml for a given value of n ? Give an example in each case.

List all the possible values of s and ms for an electron. Are there particles for which these values are different? The same?

Identify the shell, subshell, and number of electrons for the following: (a) 2p3 . (b) 4d9 . (c) 3s1 . (d) 5g16 .

Which of the following are not allowed? State which rule is violated for any that are not allowed. (a) 1p3 (b) 2p8 (c) 3g11 (d) 4 f 2

Figure shows the energy-level diagram for neon. (a) Verify that the energy of the photon emitted when neon goes from its metastable state to the one immediately below is equal to 1.96 eV. (b) Show that the wavelength of this radiation is 633 nm. (c) What wavelength is emitted when the neon makes a direct transition to its ground state?

A helium-neon laser is pumped by electric discharge. What wavelength electromagnetic radiation would be needed to pump it? See Figure for energy-level information.

Ruby lasers have chromium atoms doped in an aluminum oxide crystal. The energy level diagram for chromium in a ruby is shown in Figure What wavelength is emitted by a ruby laser? Figure 30.64 Chromium atoms in an aluminum oxide crystal have these energy levels, one of which is metastable. This is the basis of a ruby laser. Visible light can pump the atom into an excited state above the metastable state to achieve a population inversion.

(a) What energy photons can pump chromium atoms in a ruby laser from the ground state to its second and third excited states? (b) What are the wavelengths of these photons? Verify that they are in the visible part of the spectrum.

Some of the most powerful lasers are based on the energy levels of neodymium in solids, such as glass, as shown in Figure (a) What average wavelength light can pump the neodymium into the levels above its metastable state? (b) Verify that the 1.17 eV transition produces 1.06 m radiation. Figure 30.65 Neodymium atoms in glass have these energy levels, one of which is metastable. The group of levels above the metastable state is convenient for achieving a population inversion, since photons of many different energies can be absorbed by atoms in the ground state.

If an atom has an electron in the n = 5 state with ml = 3 , what are the possible values of l ?

An atom has an electron with ml = 2 . What is the smallest value of n for this electron?

What are the possible values of ml for an electron in the n = 4 state?

What, if any, constraints does a value of ml = 1 place on the other quantum numbers for an electron in an atom?

(a) Calculate the magnitude of the angular momentum for an l = 1 electron. (b) Compare your answer to the value Bohr proposed for the n = 1 state.

(a) What is the magnitude of the angular momentum for an l = 1 electron? (b) Calculate the magnitude of the electrons spin angular momentum. (c) What is the ratio of these angular momenta?

Repeat Exercise for l = 3 .

(a) How many angles can L make with the z -axis for an l = 2 electron? (b) Calculate the value of the smallest angle.

What angles can the spin S of an electron make with the z -axis?

(a) How many electrons can be in the n = 4 shell? (b) What are its subshells, and how many electrons can be in each?

(a) What is the minimum value of 1 for a subshell that has 11 electrons in it? (b) If this subshell is in the n = 5 shell, what is the spectroscopic notation for this atom?

(a) If one subshell of an atom has 9 electrons in it, what is the minimum value of l ? (b) What is the spectroscopic notation for this atom, if this subshell is part of the n = 3 shell?

(a) List all possible sets of quantum numbers n, l, ml , ms for the n = 3 shell, and determine the number of electrons that can be in the shell and each of its subshells. (b) Show that the number of electrons in the shell equals 2n2 and that the number in each subshell is 2(2l + 1) .

Which of the following spectroscopic notations are not allowed? (a) 5s1 (b) 1d1 (c) 4s3 (d) 3p7 (e) 5g15 . State which rule is violated for each that is not allowed.

Which of the following spectroscopic notations are allowed (that is, which violate none of the rules regarding values of quantum numbers)? (a) 1s1 (b) 1d3 (c) 4s2 (d) 3p7 (e) 6h20

(a) Using the Pauli exclusion principle and the rules relating the allowed values of the quantum numbers n, l, ml , ms , prove that the maximum number of electrons in a subshell is 2n2 . (b) In a similar manner, prove that the maximum number of electrons in a shell is 2n2.

Integrated Concepts Estimate the density of a nucleus by calculating the density of a proton, taking it to be a sphere 1.2 fm in diameter. Compare your result with the value estimated in this chapter.

Integrated Concepts The electric and magnetic forces on an electron in the CRT in Figure are supposed to be in opposite directions. Verify this by determining the direction of each force for the situation shown. Explain how you obtain the directions (that is, identify the rules used).

(a) What is the distance between the slits of a diffraction grating that produces a first-order maximum for the first Balmer line at an angle of 20.0 ? (b) At what angle will the fourth line of the Balmer series appear in first order? (c) At what angle will the second-order maximum be for the first line?

Integrated Concepts A galaxy moving away from the earth has a speed of 0.0100c . What wavelength do we observe for an ni = 7 to nf = 2 transition for hydrogen in that galaxy?

Integrated Concepts Calculate the velocity of a star moving relative to the earth if you observe a wavelength of 91.0 nm for ionized hydrogen capturing an electron directly into the lowest orbital (that is, a ni = to nf = 1 , or a Lyman series transition).

Integrated Concepts In a Millikan oil-drop experiment using a setup like that in Figure , a 500-V potential difference is applied to plates separated by 2.50 cm. (a) What is the mass of an oil drop having two extra electrons that is suspended motionless by the field between the plates? (b) What is the diameter of the drop, assuming it is a sphere with the density of olive oil?

Integrated Concepts What double-slit separation would produce a first-order maximum at 3.00 for 25.0-keV x rays? The small answer indicates that the wave character of x rays is best determined by having them interact with very small objects such as atoms and molecules.

Integrated Concepts In a laboratory experiment designed to duplicate Thomsons determination of qe / me , a beam of electrons having a velocity of 6.00107 m/s enters a 5.00103 T magnetic field. The beam moves perpendicular to the field in a path having a 6.80-cm radius of curvature. Determine qe / me from these observations, and compare the result with the known value.

Integrated Concepts Find the value of l , the orbital angular momentum quantum number, for the moon around the earth. The extremely large value obtained implies that it is impossible to tell the difference between adjacent quantized orbits for macroscopic objects.

Integrated Concepts Particles called muons exist in cosmic rays and can be created in particle accelerators. Muons are very similar to electrons, having the same charge and spin, but they have a mass 207 times greater. When muons are captured by an atom, they orbit just like an electron but with a smaller radius, since the mass in aB = h2 42 me kqe2 = 0.5291010 m is 207 me . (a) Calculate the radius of the n = 1 orbit for a muon in a uranium ion ( Z = 92 ). (b) Compare this with the 7.5-fm radius of a uranium nucleus. Note that since the muon orbits inside the electron, it falls into a hydrogen-like orbit. Since your answer is less than the radius of the nucleus, you can see that the photons emitted as the muon falls into its lowest orbit can give information about the nucleus.

Integrated Concepts Calculate the minimum amount of energy in joules needed to create a population inversion in a helium-neon laser containing 1.00104 moles of neon.

Integrated Concepts A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 m . In 1.00 ms, this laser raised the temperature of 1.00 cm3 of flesh to 100C and evaporated it. (a) How many photons were required? You may assume flesh has the same heat of vaporization as water. (b) What was the minimum power output during the flash?

Integrated Concepts Suppose an MRI scanner uses 100-MHz radio waves. (a) Calculate the photon energy. (b) How does this compare to typical molecular binding energies?

Integrated Concepts (a) An excimer laser used for vision correction emits 193-nm UV. Calculate the photon energy in eV. (b) These photons are used to evaporate corneal tissue, which is very similar to water in its properties. Calculate the amount of energy needed per molecule of water to make the phase change from liquid to gas. That is, divide the heat of vaporization in kJ/kg by the number of water molecules in a kilogram. (c) Convert this to eV and compare to the photon energy. Discuss the implications.

Integrated Concepts A neighboring galaxy rotates on its axis so that stars on one side move toward us as fast as 200 km/s, while those on the other side move away as fast as 200 km/s. This causes the EM radiation we receive to be Doppler shifted by velocities over the entire range of 200 km/s. What range of wavelengths will we observe for the 656.0-nm line in the Balmer series of hydrogen emitted by stars in this galaxy. (This is called line broadening.)

Integrated Concepts A pulsar is a rapidly spinning remnant of a supernova. It rotates on its axis, sweeping hydrogen along with it so that hydrogen on one side moves toward us as fast as 50.0 km/s, while that on the other side moves away as fast as 50.0 km/s. This means that the EM radiation we receive will be Doppler shifted over a range of 50.0 km/s . What range of wavelengths will we observe for the 91.20-nm line in the Lyman series of hydrogen? (Such line broadening is observed and actually provides part of the evidence for rapid rotation.)

Integrated Concepts Prove that the velocity of charged particles moving along a straight path through perpendicular electric and magnetic fields is v = E / B . Thus crossed electric and magnetic fields can be used as a velocity selector independent of the charge and mass of the particle involved.

Unreasonable Results (a) What voltage must be applied to an X-ray tube to obtain 0.0100-fm-wavelength X-rays for use in exploring the details of nuclei? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Unreasonable Results A student in a physics laboratory observes a hydrogen spectrum with a diffraction grating for the purpose of measuring the wavelengths of the emitted radiation. In the spectrum, she observes a yellow line and finds its wavelength to be 589 nm. (a) Assuming this is part of the Balmer series, determine ni , the principal quantum number of the initial state. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?

Construct Your Own Problem The solar corona is so hot that most atoms in it are ionized. Consider a hydrogen-like atom in the corona that has only a single electron. Construct a problem in which you calculate selected spectral energies and wavelengths of the Lyman, Balmer, or other series of this atom that could be used to identify its presence in a very hot gas. You will need to choose the atomic number of the atom, identify the element, and choose which spectral lines to consider.

Construct Your Own Problem Consider the Doppler-shifted hydrogen spectrum received from a rapidly receding galaxy. Construct a problem in which you calculate the energies of selected spectral lines in the Balmer series and examine whether they can be described with a formula like that in the equation 1= R 1 nf 2 1 ni 2 , but with a different constant R .