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modern physics

General Chemistry 9th edition Darrell Ebbing, Steven D. Gammon - Solutions

The first line of the Lyman series of the hydrogen atom emission results from a transition from the n = 2 level to the n = 1 level. What is the wavelength of the emitted photon? Using Figure 7.5, describe the region of the electromagnetic spectrum in which this emission lies.
What is the wavelength of the electromagnetic radiation emitted from a hydrogen atom when the electron undergoes the transition n × 5 to n × 4? In what region of the spectrum does this line occur?
Calculate the shortest wavelength of the electromagnetic radiation emitted by the hydrogen atom in undergoing a transition from the n = 6 level.
Calculate the longest wavelength of the electromagnetic radiation emitted by the hydrogen atom in undergoing a transition from the n = 7 level.
What is the difference in energy between the two levels responsible for the violet emission line of the calcium atom at 422.7 nm?
What is the difference in energy between the two levels responsible for the ultraviolet emission line of the magnesium atom at 285.2 nm? de Broglie Waves Masses of the electron, proton, and neutron are listed on the inside back cover of this book.
What is the wavelength of a neutron traveling at a speed of 4.15 km/s? (Neutrons of these speeds are obtained from a nuclear pile.)
What is the wavelength of a proton traveling at a speed of 6.58 km/s? What would be the region of the spectrum for electromagnetic radiation of this wavelength?
At what speed must an electron travel to have a wavelength of 10.0 pm?
Describe the wave–particle picture of light.
At what speed must a neutron travel to have a wavelength of 12.0 pm?
What is the de Broglie wavelength of a 145-g baseball traveling at 30.0 m/s (67.1 mph)? Is the wavelength much smaller or much larger than the diameter of an atom (on the order of 100 pm)?
What is the de Broglie wavelength of an oxygen molecule, O2, traveling at 521 m/s? Is the wavelength much smaller or much larger than the diameter of an atom (on the order of 100 pm)?
If the n quantum number of an atomic orbital is 4, what are the possible values of l? If the l quantum number is 3, what are the possible values of ml?
The n quantum number of an atomic orbital is 6. What are the possible values of l? What are the possible values of ml if the l quantum number is 5?
How many subshells are there in the M shell? How many orbitals are there in the f subshell?
How many subshells are there in the N shell? How many orbitals are there in the g subshell?
Give the notation (using letter designations for l) for the subshells denoted by the following quantum numbers. a. n = 6, l = 2 b. n = 5, l = 4 c. n = 4, l = 3 d. n = 6, l = 1
Give the notation (using letter designations for l) for the subshells denoted by the following quantum numbers. a. n = 3, l = 2 b. n = 4, l = 0 c. n = 4, l = 1 d. n = 5, l = 3
Explain why each of the following sets of quantum numbers would not be permissible for an electron, according to the rules for quantum numbers.a. n = 1, l = 0, ml = 0, ms = +1b. n = 1, l = 3, ml1 = +3, ms + 1/2c. n = 3, l = 2, ml1 = +3, ms = 1/2 d. n = 0, l = 1, ml1 = 0, ms = + 1/2 e. n = 2, l =
State which of the following sets of quantum numbers would be possible and which impossible for an electron in an atom. a. n = 2, l = 0, ml = 0, ms = + 1/2 b. n = 1, l = 1, ml = 0, ms = + 1/2 c. n = 0, l = 0, ml = 0, ms = 1/2 d. n = 2, l = 1, ml = –1, ms = 1/2 e. n = 2, l = 1, ml = –2, ms =
The blue line of the strontium atom emission has a wavelength of 461 nm. What is the frequency of this light? What is the energy of a photon of this light?
The barium atom has an emission with wavelength 554 nm (green). Calculate the frequency of this light and the energy of a photon of this light.
The energy of a photon is 4.10 × 10–19 J. What is the wavelength of the corresponding light? What is the color of this light?
The energy of a photon is 3.34 × 10–19 J. What is the wavelength of the corresponding light? What is the color of this light?
The photoelectric work function of a metal is the minimum energy needed to eject an electron by irradiating the metal with light. For calcium, this work function equals 4.34 × 10–19 J. What is the minimum frequency of light for the photoelectric effect in calcium?
The photoelectric work function for magnesium is 5.90 × 10–19 J. (The work function is the minimum energy needed to eject an electron from the metal by irradiating it with light.) Calculate the minimum frequency of light required to eject electrons from magnesium.
Light of wavelength 345 nm shines on a piece of calcium metal. What is the speed of the ejected electron? (Light energy greater than that of the work function of calcium ends up as kinetic energy of the ejected electron.
Light of wavelength 276 nm shines on a piece of magnesium metal. What is the speed of the ejected electron? (Light energy greater than that of the work function of magnesium ends up as kinetic energy of the ejected electron. See Problem 7.76 for the definition of work function and its value for
Calculate the wavelength of the Balmer line of the hydrogen spectrum in which the initial n quantum number is 5 and the final n quantum number is 2.
Physical theory at the time Rutherford proposed his nuclear model of the atom was not able to explain how this model could give a stable atom. Explain the nature of this difficulty.
Calculate the wavelength of the Balmer line of the hydrogen spectrum in which the initial n quantum number is 6 and the final n quantum number is 2.
One of the lines in the Balmer series of the hydrogen atom emission spectrum is at 397 nm. It results from a transition from an upper energy level to n = 2. What is the principal quantum number of the upper level?
A line of the Lyman series of the hydrogen atom spectrum has the wavelength 9.50 × 10–8 m. It results from a transition from an upper energy level to n = 1. What is the principal quantum number of the upper level?
A hydrogen-like ion has a nucleus of charge +Ze and a single electron outside this nucleus. The energy levels of these ions are Z2RH/n2 (where Z = atomic number). Calculate the wavelength of the transition from n × 3 to n × 2 for He+, a hydrogen-like ion. In what region of the spectrum does this
What is the wavelength of the transition from n = 5 to n = 3 for Li2+? In what region of the spectrum does this emission occur? Li2+ is a hydrogen-like ion. Such an ion has a nucleus of charge +Ze and a single electron outside this nucleus. The energy levels of the ion are Z2RH/n2, where Z is the
An electron microscope employs a beam of electrons to obtain an image of an object. What energy must be imparted to each electron of the beam to obtain a wavelength of 10.0 pm? Obtain the energy in electron volts (eV) (1 eV = 1.602 × 10–19 J).
Neutrons are used to obtain images of the hydrogen atoms in molecules. What energy must be imparted to each neutron in a neutron beam to obtain a wavelength of 10.0 pm? Obtain the energy in electron volts (eV) (1 eV = 1.602 × 10–19 J).
What is the number of different orbitals in each of the following subshells? a. 3d b. 4f c. 4p d. 5s
What is the number of different orbitals in each of the following subshells?a. 6gb. 4fc. 6sd. 5p
Explain the main features of Bohr’s theory. Do these features solve the difficulty alluded to in Question 7.8?
List the possible subshells for the n = 6 shell.
The word laser is an acronym meaning light amplification by stimulated emission of radiation. What is the stimulated emission of radiation?
Explain how lasers are used to “read” a compact disc.
Explain the concept of quantum mechanical tunneling.
Explain how the probe in a scanning tunneling microscope scans a sample on the surface of a metal.
What wavelength of electromagnetic radiation corresponds to a frequency of 7.76 × 109 s–1? Planck’s constant is 6.63 × 10–34 J•s, and the speed of light is 3.00 × 108 m/s.
AM radio stations broadcast at frequencies between 530 kHz and 1700 kHz. (1 kHz × 103 s–1.) For a station broadcasting at 1.69 × 103 kHz, what is the energy of this radio wave? Note that Planck’s constant is 6.63 × 10–34 J•s, and the speed of light is 3.00 × 108 m/s.
The photoelectric work function of a metal is the minimum energy required to eject an electron by shining light on the metal. The work function of calcium is 4.60 × 10–19 J. What is the longest wavelength of light (in nanometers) that can cause an electron to be ejected from calcium metal.
Using the Bohr formula for the energy levels, calculate the energy required to raise the electron in a hydrogen atom from n = 1 to n = ∞. Express the result for 1 mol H atoms. Because the n = ∞ level corresponds to removal of the electron from the atom, this energy equals the ionization energy
Calculate the ionization energy of the He+ ion in kJ/mol (this would be the second ionization energy of He). See Problem 8.107. The Bohr formula for the energy levels of an ion consisting of a nucleus of charge Z and a single electron is RHZ2/n2. Problem 8.107 Using the Bohr formula for the energy
The lattice energy of an ionic solid such as NaCl is the enthalpy change ˆ†H° for the process in which the solid changes to ions. For example,NaCl(s) †’ Na+(g) + Cl(g) ˆ†H = 786 kJ/molAssume that the ionization energy and electron affinity are ˆ†H values
Describe the major trends that emerge when atomic radii are plotted against atomic number. Describe the trends observed when first ionization energies are plotted against atomic number.
Calculate ˆ†H for the following process:K(g) + Br(g) †’ KBr(s)The lattice energy of KBr is 689 kJ/mol, and the ionization energy of K is 419 kJ/mol. The electron affinity of Br is given in Table 8.4. See Problem 8.109.Problem 8.109The lattice energy of an ionic solid such as
What main group in the periodic table has elements with the most negative electron affinities for each period? What electron configurations of neutral atoms have only unstable negative ions?
The ions Na+ and Mg2+ occur in chemical compounds, but the ions Na2+ and Mg3+ do not. Explain.
List the elements in Groups IIIA to VIA in the same order as in the periodic table. Label each element as a metal, a metalloid, or a nonmetal. Does each column of elements display the expected trend of increasing metallic characteristics?
Describe the model of electron spin given in the text. What are the restrictions on electron spin?
For the list of elements you made for Question 8.19, note whether the oxides of each element are acidic, basic, or amphoteric.
From what is said in Section 8.7 about Group IIA elements, list some properties of barium.
Match each description in the left column with the appropriate element in the right column. a. A waxy, white solid, normally stored under water ………… Sulfur b. A yellow solid that burns in air …………………………. … Sodium c. A reddish brown liquid
A hypothetical element, X, has the following ionization energy values: First ionization energy: 900 kJ/mol Second ionization energy: 1750 kJ/mol Third ionization energy: 14,900 kJ/mol Fourth ionization energy: 21,000 kJ/mol Another element,Y, has the following ionization energy values: First
How does the Pauli exclusion principle limit the possible electron configurations of an atom?
Consider two hypothetical elements, W and Z. Element W has an electron affinity of 300 kJ/mol, and element Z has an electron affinity of 75 kJ/mol. a. If you have a W ion and a Z ion, from which ion would it require more energy to remove an electron? Explain your answer. b. If elements W and Z
Suppose that the Pauli exclusion principle were “No more than two electrons can have the same four quantum numbers.” What would be the electron configurations of the ground states for the first six elements of the periodic table, assuming that, except for the Pauli principle, the usual
Imagine a world in which all quantum numbers, except the l quantum number, are as they are in the real world. In this imaginary world, l begins with l and goes up to n (the value of the principal quantum number). Assume that the orbitals fill in the order by n, then l; that is, the first orbital to
You travel to an alternate universe where the atomic orbitals are different from those on earth, but all other aspects of the atoms are the same. In this universe, you find that the first (lowest energy) orbital is filled with three electrons and the second orbital can hold a maximum of nine
Would you expect to find an element having both a very large (positive) first ionization energy and an electron affinity that is much less than zero (large but negative)? Explain.
Two elements are in the same group, one following the other. One is a metalloid; the other is a metal. Both form oxides of the formula RO2. The first is acidic; the next is amphoteric. Identify the two elements.
A metalloid has an acidic oxide of the formula R2O3. The element has no oxide of the formula R2O5. What is the name of the element?
Given the following information, identify the group from the periodic table that contains elements that behave like main-group element “E.” (i) The electron affinity of E is greater than zero. (ii) The ionization energy (IE) trend for element E is: first ionization energy < second ionization
What is the maximum number of electrons that can occupy a g subshell (l = 4)?
A hypothetical element A has the following properties: First ionization energy: 850 kJ/mol Second ionization energy: 1700 kJ/mol Third ionization energy: 13,999 kJ/mol a. If you were to react element A with oxygen, what would be the chemical formula of the resulting compound? b. Write the balanced
Which of the following orbital diagrams are allowed by the Pauli exclusion principle? Explain how you arrived at this decision. Give the electron configuration for the allowed ones.a.b. c. d.
Which of the following orbital diagrams are allowed and which are not allowed by the Pauli exclusion principle? Explain. For those that are allowed, write the electron configuration.a.b. c. d.
Which of the following electron configurations are possible? Explain why the others are not. a. 1s12s22p7 b. 1s22s22p63s33d7 c. 1s22s22p5 d. 1s22s22p63s23d8
Choose the electron configurations that are possible from among the following. Explain why the others are impossible. a. 1s22s12p6 b. 1s22s22p8 c. 1s22s32p63s23p63d7 d. 1s22s22p63s13d9
Write all of the possible orbital diagrams for the electron configuration 1s22p1. (There are six different diagrams.)
Give the different orbital diagrams for the configuration 1s12p1. (There are twelve different diagrams.)
Thallium has the ground-state configuration [Xe]4f145d106s26p1. Give the group and period for this element. Classify it as a main-group, a d-transition, or an f-transition element.
The configuration for the ground state of iridium is [Xe]4f145d76s2. What are the group and period for this element? Is it a main-group, a d-transition, or an f-transition element?
Write the orbital diagram for the ground state of cobalt. The electron configuration is [Ar]3d74s2.
Write the orbital diagram for the ground state of terbium. The electron configuration is [Xe]4f96s2.
Write an orbital diagram for the ground state of the potassium atom. Is the atomic substance diamagnetic or paramagnetic?
Define each of the following: noble-gas core, pseudo-noble-gas core, valence electron.
Write an orbital diagram for the ground state of the calcium atom. Is the atomic substance diamagnetic or paramagnetic?
Order the following elements by increasing atomic radius according to what you expect from periodic trends: Se, S, As.
Using periodic trends, arrange the following elements in order of increasing atomic radius: O, P, S.
Arrange the following elements in order of increasing ionization energy: Mg, Ca, S. Do not look at Figure 8.18.
From what you know in a general way about electron affinities, state which member of each of the following pairs has the greater negative value: (a) As, Br (b) F, Li.
From what you know in a general way about electron affinities, state which member of each of the following pairs has the greater negative value: (a) Cl, S (b) Se, K.
If potassium chlorate has the formula KClO3, what formula would you expect for lithium bromate?
Give two different possible orbital diagrams for the 1s22s22p4 configuration of the oxygen atom, one of which should correspond to the ground state. Label the diagram for the ground state.
Write the orbital diagram for the ground state of the arsenic atom. Give all orbitals.
Write the orbital diagram for the ground state of the germanium atom. Give all orbitals.
Write the orbital diagram corresponding to the ground state of Nb, whose configuration is [Kr]4d45s1.
Define the terms diamagnetic substance and paramagnetic substance. Does the ground-state oxygen atom give a diamagnetic or a paramagnetic substance? Explain.
Write the orbital diagram for the ground state of ruthenium. The configuration is [Kr]4d75s1.
Find the electron configuration of the element with Z = 23. From this, give its group and period in the periodic table. Classify the element as a main-group, a d-block transition, or an f-block transition element.
Find the electron configuration of the element with Z = 33. From this, give its group and period in the periodic table. Is this a main-group, a d-block transition, or an f-block transition element?

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