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chemistry a molecular approach

Chemistry A Molecular Approach 5th Edition Nivaldo Tro - Solutions

What are complementary properties? How does electron diffraction demonstrate the complementarity of the wave nature and particle nature of the electron?
Explain Heisenberg’s uncertainty principle. What paradox is at least partially solved by the uncertainty principle?
An electron behaves in ways that are at least partially indeterminate.Explain this statement.
What is a probability distribution map?
For each solution to the Schrödinger equation, what can be precisely specified: the electron’s energy or its position? Explain.
What is a quantum-mechanical orbital?
What is the Schrödinger equation? What is a wave function?How is a wave function related to an orbital?
What are the possible values of the principal quantum number n? What does the principal quantum number determine?
What are the possible values of the angular momentum quantum number l? What does the angular momentum quantum number determine?
What are the possible values of the magnetic quantum number ml? What does the magnetic quantum number determine?
List all the orbitals in each principal level. Specify the three quantum numbers for each orbital.a. n = 1 b. n = 2 c. n = 3 d. n = 4
Explain the difference between a plot showing the probability density for an orbital and one showing the radial distribution function.
Make sketches of the general shapes of the s, p, and d orbitals.
List the four different sublevels associated with n = 4. Given that only a maximum of two electrons can occupy an orbital, determine the maximum number of electrons that can exist in each sublevel.
Why are atoms usually portrayed as spheres when most orbitals are not spherically shaped?
The distance from the sun to Earth is 1.496 * 108 km. How long does it take light to travel from the sun to Earth?
The nearest star to our sun is Proxima Centauri, at a distance of 4.3 light-years from the sun. A light-year is the distance that light travels in one year (365 days). How far away, in km, is Proxima Centauri from the sun?
List these types of electromagnetic radiation in order of (i) Increasing wavelength and (ii) Increasing energy per photon.a. Radio waves b. Microwavesc. Infrared radiation d. Ultraviolet radiation
List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon.a. Gamma rays b. Radio wavesc. Microwaves d. Visible light
Calculate the energy of a photon of electromagnetic radiation at each of the wavelengths indicated in Problem 39.Problem 39Calculate the frequency of each wavelength of electromagnetic radiation.a. 632.8 nm (wavelength of red light from helium–neon laser)b. 503 nm (wavelength of maximum solar
Calculate the wavelength of each frequency of electromagnetic radiation.a. 100.2 MHz (typical frequency for FM radio broadcasting)b. 1070 kHz (typical frequency for AM radio broadcasting)c. 835.6 MHz (common frequency used for cell phone communication)
Calculate the energy of a photon of electromagnetic radiation at each of the frequencies indicated in Problem 40.Problem 40Calculate the wavelength of each frequency of electromagnetic radiation.a. 100.2 MHz (typical frequency for FM radio broadcasting)b. 1070 kHz (typical frequency for AM radio
A laser pulse with wavelength 532 nm contains 3.85 mJ of energy. How many photons are in the laser pulse?
A heat lamp produces 32.8 watts of power at a wavelength of 6.5 mm. How many photons are emitted per second?
Determine the energy of 1 mol of photons for each kind of light.a. Infrared radiation (1500 nm)b. Visible light (500 nm)c. Ultraviolet radiation (150 nm)
How much energy is contained in 1 mol of each?a. X-ray photons with a wavelength of 0.135 nmb. G-ray photons with a wavelength of 2.15 * 10-5 nm
Sketch the interference pattern that results from the diffraction of electrons passing through two closely spaced slits.
What happens to the interference pattern described in Problem 47 if the rate of electrons going through the slits is decreased to one electron per hour? What happens to the pattern if we try to determine which slit the electron goes through by using a laser placed directly behind the slits?Problem
The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron
The smallest atoms can themselves exhibit quantum-mechanical behavior. Calculate the de Broglie wavelength (in pm) of a hydrogen atom traveling at 475 m/s.
What is the de Broglie wavelength of an electron traveling at 1.35 * 105 m/s?
The iodine molecule can be photodissociated (broken apart with light) into iodine atoms in the gas phase with light of wavelengths shorter than about 792 nm. A 100.0-mL glass tube contains 55.7 mtorr of gaseous iodine at 25.0 °C. What minimum amount of light energy must be absorbed by the iodine
A 5.00-mL ampule of a 0.100-M solution of naphthalene in hexane is excited with a flash of light. The naphthalene emits 15.5 J of energy at an average wavelength of 349 nm. What percentage of the naphthalene molecules emitted a photon?
Choose the larger atom or ion from each pair.(a) S or S2– (b) Ca or Ca2+ (c) Br– or Kr
Which statement is true about effective nuclear charge?a) Effective nuclear charge decreases as you move to the right across a row in the periodic table.b) Effective nuclear charge increases as you move to the right across a row in the periodic table.c) Effective nuclear charge remains constant as
What is Coulomb’s law? Explain how the potential energy of two charged particles depends on the distance between the charged particles and on the magnitude and sign of their charges.
On the basis of periodic trends, determine which element in each pair has the higher first ionization energy (if possible).(a) Al or S (b) As or Sb (c) N or Si (d) O or Cl
A proton in a linear accelerator has a de Broglie wavelength of 122 pm. What is the speed of the proton?
Calculate the de Broglie wavelength of a 143-g baseball traveling at 95 mph. Why is the wave nature of matter not important for a baseball?
A 0.22-caliber handgun fires a 1.9-g bullet at a velocity of 765 m/s. Calculate the de Broglie wavelength of the bullet. Is the wave nature of matter significant for bullets?
An electron has an uncertainty in its position of 552 pm. What is the minimum uncertainty in its velocity?
Which electron is, on average, closer to the nucleus: an electron in a 2s orbital or an electron in a 3s orbital?
Which electron is, on average, farther from the nucleus: an electron in a 3p orbital or an electron in a 4p orbital?
What are the possible values of l for each value of n?a. 1 b. 2 c. 3 d. 4
What are the possible values of ml for each value of l?a. 0 b. 1 c. 2 d. 3
Which set of quantum numbers cannot specify an orbital?a. n = 2, l = 1, ml = -1 b. n = 3, l = 2, ml = 0c. n = 3, l = 3, ml = 2 d. n = 4, l = 3, ml = 0
Which combinations of n and l represent real orbitals, and which do not exist?a. 1s b. 2p c. 4s d. 2d
Sketch the 1s and 2p orbitals. How do the 2s and 3p orbitals differ from the 1s and 2p orbitals?
Determine whether each transition in the hydrogen atom corresponds to absorption or emission of energy. a. n = 3n = 1 b. n = 2n = 4 c. n = 4 n = 3
Sketch the 3d orbitals. How do the 4d orbitals differ from the 3d orbitals?
An electron in a hydrogen atom is excited with electrical energy to an excited state with n = 2. The atom then emits a photon.What is the value of n for the electron following the emission?
According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 2p → 1s or 3p → 1s?
According to the quantum-mechanical model for the hydrogen atom, which electron transition produces light with the longer wavelength: 3p → 2s or 4p → 3p?
Calculate the wavelength of the light emitted when an electron in a hydrogen atom makes each transition and indicate the region of the electromagnetic spectrum (infrared, visible, ultraviolet, etc.) where the light is found.a. n = 2 → n = 1 b. n = 3 → n = 1c. n = 4 → n = 2 d. n = 5 → n = 2
Calculate the frequency of the light emitted when an electron in a hydrogen atom makes each transition.a. n = 4 → n = 3 b. n = 5 → n = 1c. n = 5 → n = 4 d. n = 6 → n = 5
An electron in the n = 7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. What is the value of n for the level to which the electron relaxed?
An electron in a hydrogen atom relaxes to the n = 4 level, emitting light of 114 THz. What is the value of n for the level in which the electron originated?
The human eye contains a molecule called 11-cis-retinal that changes shape when struck with light of sufficient energy. The change in shape triggers a series of events that result in an electrical signal being sent to the brain that results in vision. The minimum energy required to change the
An argon ion laser puts out 5.0 W of continuous power at a wavelength of 532 nm. The diameter of the laser beam is 5.5 mm. If the laser is pointed toward a pinhole with a diameter of 1.2 mm, how many photons travel through the pinhole per second?Assume that the light intensity is equally
In a technique used for surface analysis called Auger electron spectroscopy (AES), electrons are accelerated toward a metal surface. These electrons cause the emissions of secondary electrons—called Auger electrons—from the metal surface. The kinetic energy of the Auger electrons depends on the
A green leaf has a surface area of 2.50 cm2. If solar radiation is 1000 W/m2, how many photons strike the leaf every second?Assume three significant figures and an average wavelength of 504 nm for solar radiation.
An X-ray photon of wavelength 0.989 nm strikes a surface. The emitted electron has a kinetic energy of 969 eV. What is the binding energy of the electron in kJ/mol? [1 electron volt (eV) = 1.602 x 10-19 J]
Ionization involves completely removing an electron from an atom. How much energy is required to ionize a hydrogen atom in its ground (or lowest energy) state? What wavelength of light contains enough energy in a single photon to ionize a hydrogen atom?
The energy required to ionize sodium is 496 kJ/mol. What minimum frequency of light is required to ionize sodium?
Suppose that, in an alternate universe, the possible values of ml are the integer values including 0 ranging from -l - 1 to l + 1 (instead of simply -l to +l). How many orbitals exist in each sublevel in the alternate universe?a. s sublevel b. p sublevel c. d sublevel
An atomic emission spectrum of hydrogen shows three wavelengths: 1875 nm, 1282 nm, and 1093 nm. Assign these wavelengths to transitions in the hydrogen atom.
Suppose that in an alternate universe, the possible values of l are the integer values from 0 to n (instead of 0 to n - 1). Assuming no other differences between this imaginary universe and ours, how many orbitals exist in each level in the alternate universe?a. n = 1 b. n = 2 c. n = 3
An atomic emission spectrum of hydrogen shows three wavelengths: 121.5 nm, 102.6 nm, and 97.23 nm. Assign these wavelengths to transitions in the hydrogen atom.
The binding energy of electrons in a metal is 193 kJ/mol. Find the threshold frequency of the metal.
In order for a thermonuclear fusion reaction of two deuterons (21 H+) to take place, the deuterons must collide and each must have a velocity of about 1 * 106 m/s. Find the wavelength of such a deuteron.
The speed of sound in air is 344 m/s at room temperature. The lowest frequency of a large organ pipe is 30 s-1 and the highest frequency of a piccolo is 1.5 * 104 s-1. Find the difference in wavelength between these two sounds.
The distance from Earth to the sun is 1.5 * 108 km. Find the number of crests in a light wave of frequency 1.0 * 1014 s-1 traveling from the sun to Earth.
The quantum yield of light-induced chemical reactions (called photochemical reactions) measures the efficiency of the process. The quantum yield, f, is defined as:for the reaction CH3X → CH3 + X is ϕ = 0.24. A cuvette containing a solution of CH3X is irradiated with 280-nm light with a power of
A particular laser consumes 150.0 watts of electrical power and produces a stream of 1.33 * 1019 1064-nm photons per second.What is the percent efficiency of the laser in converting electrical power to light?
A student is studying the photodissociation (dissociation with light) of I2 → 2 I. When a sample of I2 is irradiated with a power of 255 mW at 590 nm for 35 seconds, 0.0256 mmol of I forms. Assuming complete absorption of the incident radiation, what is the quantum yield, ϕ, of the
An electron confined to a one-dimensional box has energy levels given by the equation:where n is a quantum number with possible values of 1, 2, 3, c, m is the mass of the particle, and L is the length of the box.a. Calculate the energies of the n = 1, n = 2, and n = 3 levels for an electron in a
The energy of a vibrating molecule is quantized much like the energy of an electron in the hydrogen atom. The energy levels of a vibrating molecule are given by the equation:where n is a quantum number with possible values of 1, 2, c, and n is the frequency of vibration. The vibration frequency of
The wave functions for the 1s and 2s orbitals are as follows:where a0 is a constant (a0 = 53 pm) and r is the distance from the nucleus. Use a spreadsheet to make a plot of each of these wave functions for values of r ranging from 0 pm to 200 pm.Describe the differences in the plots and identify
Before quantum mechanics was developed, Johannes Rydberg developed an equation that predicted the wavelengths (l) in the atomic spectrum of hydrogen:In this equation, R is a constant and m and n are integers. Use the quantum-mechanical model for the hydrogen atom to derive the Rydberg equation. 1/A
Find the velocity of an electron emitted by a metal with a threshold frequency of 2.25 * 1014 s-1 when it is exposed to visible light of wavelength 5.00 * 10-7 m.
Water is exposed to infrared radiation of wavelength 2.8 * 10-4 cm. Assume that all the radiation is absorbed and converted to heat. How many photons are required to raise the temperature of 2.0 g of water by 2.0 K?
The 2005 Nobel Prize in Physics was given, in part, to scientists who had made ultrashort pulses of light. These pulses are important in making measurements involving very short time periods. One challenge in making such pulses is the uncertainty principle, which can be stated with respect to
A metal with a threshold frequency of 6.71 * 1014 s-1 emits an electron with a velocity of 6.95 * 105 m/s when radiation of 1.01 * 1015 s-1 strikes the metal. Calculate the mass of the electron.
Find the longest wavelength of a wave that can travel around in a circular orbit of radius 1.8 m.
The heat of fusion of ice is 6.00 kJ/mol. Find the number of photons of wavelength = 6.42 * 10-6 m that must be absorbed to melt 1.00 g of ice.
Explain the difference between the Bohr model for the hydrogen atom and the quantum-mechanical model. Is the Bohr model consistent with Heisenberg’s uncertainty principle?
The light emitted from one of the following electronic transitions (n = 4 → n = 3 or n = 3 → n = 2) in the hydrogen atom causes the photoelectric effect in a particular metal, while light from the other transition does not. Which transition causes the photoelectric effect and why?
Which transition in the hydrogen atom produces emitted light with the longest wavelength? a. n = 4- n = 3 b. n = 2n=1 1 c. n = 3n = 2
Determine whether an interference pattern is observed on the other side of the slits in each experiment.a. An electron beam is aimed at two closely spaced slits. The beam produces only one electron per minute.b. An electron beam is aimed at two closely spaced slits. A light beam is placed at each
Discuss the nature of light with your group. Ask each member of your group to transcribe one complete sentence about the physical nature of light.
How are electrons like baseballs? How are they unlike baseballs?
What are all the possible values of ml if l = 0 (an s orbital)? If l = 1 (a p orbital)? If l = 2 (a d orbital)? How many possible values of ml would there be if l = 20? Write an equation to determine the number of possible values of ml from the value of l.
Sunscreen contains compounds that absorb ultraviolet light. When sunscreen is applied to skin, it prevents ultraviolet light from reaching the skin. The graph that follows shows the absorbance of light as a function of wavelength for two different compounds (2-EHMC and TDSA) common in sunscreen.
Have each group member choose a set of quantum numbers for an electron in a hydrogen atom. Calculate the wavelength of light produced if an electron moves from your state to each state of the other group members. Make a table comparing all possible combinations, and list all wavelengths in order of
How many nodes are there in the 1s, 2p, and 3d orbitals? How many nodes are in a 4f orbital?
According to Coulomb’s law, what happens to the potential energy of two oppositely charged particles as they get closer together?(a) Their potential energy decreases.(b) Their potential energy increases.(c) Their potential energy does not change.
According to Coulomb’s law, if the separation between two particles of the same charge is doubled, what happens to the potential energy of the two particles?a) It is twice as high as it was before the distance separation.b) It is one-half as high as it was before the separation.c) It does not
What are periodic properties?
Write electron configurations for each element.(a) Mg (b) P (c) Br (d) Al
Which statement is true?(a) An orbital that penetrates into the region occupied by core electrons is more shielded from nuclear charge than an orbital that does not penetrate and therefore has a higher energy.(b) An orbital that penetrates into the region occupied by core electrons is less shielded

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