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general chemistry principles

General Chemistry Principles And Modern Applications 11th Edition Ralph Petrucci, Jeffry Madura, F. Herring, Carey Bissonnette - Solutions

How would the Balmer equation (8.4) have to be modified to predict lines in the infrared spectrum of hydrogen?Eq. 8.4 1 4/1 1 - = - 3 (→ ) - ²+(²² - 2) RH A B 2 m² nº m (8.4)
What is ΔE for the transition of an electron from n = 6 to n = 3 in a hydrogen atom? What is the frequency of the spectral line produced?
To what value of n in equation (8.4) does the line in the Balmer series at 389 nm correspond?Eq. 8.4 入 (六) B\n² = RH (8.4)
What is ΔE for the transition of an electron from n = 5 to n = 2 in a hydrogen atom? What is the frequency of the spectral line produced?
The Lyman series of the hydrogen spectrum can be represented by the equation(a) Calculate the maximum and minimum wavelength lines, in nanometers, in this series.(b) What value of n corresponds to a spectral line at 95.0 nm?(c) Is there a line at 108.5 nm? Explain. v = 3.2881 x 10¹5 s
Calculate the wavelengths, in nanometers, of the first four lines of the Balmer series of the hydrogen spectrum, starting with the longest wavelength component.
A line is detected in the hydrogen spectrum at 1880 nm. Is this line in the Balmer series? Explain.
Calculate the energy, in joules, of a hydrogen atom when the electron is in the sixth energy level.
Calculate the increase in energy, in joules, when an electron in the hydrogen atom is excited from the first to the third energy level.
What are the (a) Frequency, in s-1, and (b) Wavelength, in nanometers, of the light emitted when the electron in a hydrogen atom drops from the energy level n = 7 to n = 4?(c) In what portion of the electromagnetic spectrum is this light?
Without doing detailed calculations, indicate which of the following electron transitions requires the greatest amount of energy to be absorbed by a hydrogen atom: from (a) n = 1 to n = 2; (b) n = 2 to n = 4; (c) n = 3 to n = 9;(d) n = 10 to n = 1.
For a hydrogen atom, determine (a) The energy level corresponding to n = 8;(b) Whether there is an energy level at -2.500 x 10-19 J;(c) The ionization energy, if the electron is initially in the n = 6 level.
Without doing detailed calculations, indicate which of the following electron transitions in the hydrogen atom results in the emission of light of the longest wavelength. (a) n = 4 to n = 3;(b) n = 1 to n = 2;(c) n = 1 to n = 6;(d) n = 3 to n = 2.
What electron transition in a hydrogen atom, starting from n = 7, will produce light of wavelength 410 nm?
The emission spectrum below for a one-electron (hydrogen-like) species in the gas phase shows all the lines, before they merge together, resulting from transitions to the ground state from higher energy states. Line A has a wavelength of 103 nm.(a) What are the upper and lower principal quantum
What electron transition in a hydrogen atom, ending in n = 3, will produce light of wavelength 1090 nm?
The emission spectrum below for a one-electron (hydrogen-like) species in the gas phase shows all the lines, before they merge together, resulting from transitions to the first excited state from higher energy states. Line A has a wavelength of 434 nm.(a) What are the upper and lower principal
The emission spectrum below for a one-electron (hydrogen-like) species in the gas phase shows all the lines, before they merge together, resulting from transitions to the first excited state from higher energy states. Line A has a wavelength of 27.1 nm.(a) What are the upper and lower principal
The emission spectrum below for a one-electron (hydrogen-like) species in the gas phase shows all the lines, before they merge together, resulting from transitions to the ground state from higher energy states. Line A has a wavelength of 10.8 nm.(a) What are the upper and lower principal quantum
Which must possess a greater velocity to produce matter waves of the same wavelength (such as 1 nm), protons or electrons? Explain your reasoning.
What must be the velocity, in meters per second, of a beam of electrons if they are to display a de Broglie wavelength of 850 nm?
Calculate the de Broglie wavelength, in nanometers, associated with a 145 g baseball traveling at a speed of 168 km/h. How does this wavelength compare with typical nuclear or atomic dimensions?
The uncertainty relation ΔxΔp ≥ h/(4π), expression (8.11), is valid for motion in any direction. For circular motion, the relation may be expressed as ΔrΔp ≥ h/(4π), where Δr is the uncertainty in radial position and Δp is the uncertainty in the momentum along the radial direction.
What is the wavelength, in nanometers, associated with a 9.7 g bullet with a muzzle velocity of 887 m s-1, that is, considering the bullet to be a matter wave? Comment on the feasibility of an experimental measurement of this wavelength.
Although Einstein made some early contributions to quantum theory, he was never able to accept the Heisenberg uncertainty principle. He stated, “God does not play dice with the Universe.” What do you suppose Einstein meant by this remark? In reply to Einstein’s remark, Niels Bohr is supposed
A proton is accelerated to one-tenth the velocity of light, and this velocity can be measured with a precision of 1%. What is the uncertainty in the position of this proton?
Show that the uncertainty principle is not significant when applied to large objects such as automobiles. Assume that m is precisely known; assign a reasonable value to either the uncertainty in position or the uncertainty in velocity, and estimate a value of the other.
What must be the velocity of electrons if their associated wavelength is to equal the Bohr radius, a0?
What must be the velocity of electrons if their associated wavelength is to equal the longest wavelength line in the Lyman series?
A standing wave in a string 42 cm long has a total of six nodes (including those at the ends). What is the wavelength, in centimeters, of this standing wave?
What is the length of a string that has a standing wave with four nodes (including those at the ends) and λ = 17 cm?
Calculate the wavelength of the electromagnetic radiation required to excite an electron from the ground state to the level with n = 4 in a one-dimensional box 5.0 x 101 pm long.
An electron in a one-dimensional box requires a wavelength of 618 nm to excite an electron from the n = 2 level to the n = 4 level. Calculate the length of the box.
An electron in a 20.0 nm box is excited from the ground state into a higher energy state by absorbing a photon of wavelength 8.60 x 10-5 m. Determine the final energy state.
Calculate the wavelength of the electromagnetic radiation required to excite a proton from the ground state to the level with n = 4 in a one-dimensional box 5.0 x 101 pm long.
Describe some of the differences between the orbits of the Bohr atom and the orbitals of the wave mechanical atom. Are there any similarities?
Select the correct answer and explain your reasoning. An electron having n = 3 and me = 0 (a) must have 1 ms =+; (b) must have l = 1; (c) may have € = 0, 1, 2' or 2; (d) must have l = 2.
The greatest probability of finding the electron in a small-volume element of the 1s orbital of the hydrogen atom is at the nucleus. Yet the most probable distance of the electron from the nucleus is 53 pm. How can you reconcile these two statements?
Write an acceptable value for each of the missing quantum numbers. (a) n = 3, (b) n (c) n = 4, l = (d) n = ?, l= ?, l = ?, me = 2, ms 2, me = 1, ms 2, me 0, me = = 0, ms ?, ms ? = ? 1 1 2
What type of orbital (i.e., 3s, 4p, . . . ) is designated by these quantum numbers? (a) n = 5, l = 1, me = 0 (b) n = 4, l = 2, me = -2 (c) n = 2, l = 0, me = 0
Concerning the electrons in the shells, subshells, and orbitals of an atom, how many can have mg 1, and m² = +- ? (a) n = 4, = 2, me = 1, and (b) n = 4, l = 2, and me = 1? (c) n = 4 and l = 2? (d) n = 4? 1 (e) n = 4, l = 2, and m, = +=?
Which of the following statements is (are) correct for an electron with n = 4 and mℓ = 2? Explain.(a) The electron is in the fourth principal shell.(b) The electron may be in a d orbital.(c) The electron may be in a p orbital.(d) The electron must have ms = +1/2.
Concerning the concept of subshells and orbitals, (a) How many subshells are found in the n = 3 level?(b) What are the names of the subshells in the n = 3 level?(c) How many orbitals have the values n = 4 and ℓ = 3?(d) How many orbitals have the values n = 3, ℓ = 2, and mℓ = -2?(e) What is
Calculate the finite value of r, in terms of a0, at which the node occurs in the wave function of the 2s orbital of a hydrogen atom.
Calculate the finite value of r, in terms of a0, at which the node occurs in the wave function of the 2s orbital of a Li2+ ion.
Show that the probability of finding a 2py electron in the xz plane is zero.
Show that the probability of finding a 3dxz electron in the xy plane is zero.
Prepare a two-dimensional plot of ϒ(θ, ϕ) for the py orbital in the xy plane.
Prepare a two-dimensional plot of for ϒ2(θ, ϕ) the py orbital in the xy plane.
Using a graphical method, show that in a hydrogen atom the radius at which there is a maximum probability of finding an electron is a0 (53 pm).
Use a graphical method or some other means to show that in a Li2+ ion, the radius at which there is a maximum probability of finding an electron is a0/3 (18 pm).
Identify the orbital that has (a) One radial node and one angular node; (b) No radial nodes and two angular nodes; (c) Two radial nodes and three angular nodes.
A contour map for an atomic orbital of hydrogen is shown at the top of page 370 for the xy and xz planes. Identify the orbital. G z axis G xy plane xaxis y axis
Identify the orbital that has (a) Two radial nodes and one angular node; (b) Five radial nodes and zero angular nodes; (c) One radial node and four angular nodes.
A contour map for an atomic orbital of hydrogen is shown below for the xy and xz planes. Identify the type (s, p, d, ƒ, g . . . ) of orbital. y axis x axis z axis 2 CO xy plane
On the basis of the periodic table and rules for electron configurations, indicate the number of (a) 2p electrons in N; (b) 4s electrons in Rb; (c) 4d electrons in As; (d) 4f electrons in Au; (e) Unpaired electrons in Pb; (f) Elements in group 14 of the periodic table;(g) Elements in the
Which of the following is the correct orbital diagram for the ground-state electron configuration of phosphorus? Explain what is wrong with each of the others. (a) [Ne] 3s (b) [Ne] 14 3s (c) [Ne] (d) [Ne] 3s 3.s 11 3р 3р 3р 3р
Based on the relationship between electron configurations and the periodic table, give the number of (a) Outer-shell electrons in an atom of Sb; (b) Electrons in the fourth principal electronic shell of Pt; (c) Elements whose atoms have six outer-shell electrons; (d) Unpaired electrons in an
Which of the following is the correct orbital diagram for the ground-state electron configuration of molybdenum? Explain what is wrong with each of the others. (a) [Ar] (b) [Kr] (c) [Kr] (d) [Ar] NNNNN 3d 4d 4d 3d 5s 5s 3f 4s N1 4p 4d
Use the basic rules for electron configurations to indicate the number of (a) Unpaired electrons in an atom of P; (b) 3d electrons in an atom of Br; (c) 4p electrons in an atom of Ge; (d) 6s electrons in an atom of Ba;(e) 4ƒ electrons in an atom of Au.
Use orbital diagrams to show the distribution of electrons among the orbitals in (a) The 4p subshell of Br;(b) The 3d subshell of Co2+, given that the two electrons lost are 4s; (c) The 5d subshell of Pb.
The recently discovered element 114, Flerovium, should most closely resemble Pb.(a) Write the electron configuration of Pb.(b) Propose a plausible electron configuration for element 114.
Without referring to any tables or listings in the text, mark an appropriate location in the blank periodic table provided for each of the following: (a) The fifth-period noble gas; (b) A sixth-period element whose atoms have three unpaired p electrons; (c) A d-block element having one 4s
Which of the following electron configurations corresponds to the ground state and which to an excited state? (a) [B] (b) [C] (c) [N] (d) [O] 1s 25 N N 1s 25 2p 2p 1s 25 2p N N ^^ 1s 2s 2p
To what neutral atom do the following valence-shell configurations correspond? Indicate whether the configuration corresponds to the ground state or an excited state. (a) (b) (с) (d) 3.s 3s 3s N N 3.s 3р 3р 3p 3р
What is the expected ground-state electron configuration for each of the following elements? (a) Mercury;(b) Calcium; (c) Polonium; (d) Tin; (e) Tantalum;(f) Iodine.
What is the expected ground-state electron configuration for each of the following elements? (a) Tellurium;(b) Cesium; (c) Selenium; (d) Platinum;(e) Osmium;(f) Chromium.
The following electron configurations correspond to the ground states of certain elements. Name each element.(a) [Rn]6d27s2;(b) [He]2s22p2;(c) [Ar]3d34s2;(d) [Kr]4d105s25p4;(e) [Xe]4ƒ26s26p1.
The following electron configurations correspond to the ground states of certain elements. Name each element.(a) [Ar]3d104s24p3;(b) [Ne]3s23p4;(c) [Ar]3d14s2;(d) [Kr]4d65s2; (e) [Xe]4ƒ126s2.
Derive the Balmer and Rydberg equations from equation (8.6).Eq. 8.6 AE = E₁ - E₁ -RH n² - RH n = -RH nf 1 nj (8.6)
Electromagnetic radiation can be transmitted through a vacuum or empty space. Can heat be similarly transferred? Explain.
The work function is the energy that must be supplied to cause the release of an electron from a photoelectric material. The corresponding photon frequency is the threshold frequency. The higher the energy of the incident light, the more kinetic energy the electrons have in moving away from the
Infrared lamps are used in cafeterias to keep food warm. How many photons per second are produced by an infrared lamp that consumes energy at the rate of 95 W and is 14% efficient in converting this energy to infrared radiation? Assume that the radiation has a wavelength of 1525 nm.
In 5.0 s, a 75 watt light source emits 9.91 x 1020 photons of a monochromatic (single wavelength) radiation. What is the color of the emitted light?
Determine the de Broglie wavelength of the electron ionized from a He+ ion in its ground state using light of wavelength 208 nm.
The Pfund series of the hydrogen spectrum has as its longest wavelength component a line at 7400 nm. Describe the electron transitions that produce this series. That is, give a quantum number that is common to this series.
Between which two levels of the hydrogen atom must an electron fall to produce light of wavelength 1876 nm?
Use appropriate relationships from the chapter to determine the wavelength of the line in the emission spectrum of He+ produced by an electron transition from n = 5 to n = 2.
Draw an energy-level diagram that represents all the possible lines in the emission spectrum of hydrogen atoms produced by electron transitions, in one or more steps, from n = 5 to n = 1.
An atom in which just one of the outer-shell electrons is excited to a very high quantum level n is called a “high Rydberg” atom. In some ways, all these atoms resemble a hydrogen atom with its electron in a high n level. Explain why you might expect this to be the case.
If all other rules governing electron configurations were valid, what would be the electron configuration of cesium if(a) There were three possibilities for electron spin; (b) The quantum number ℓ could have the value n?
Ozone, O3, absorbs ultraviolet radiation and dissociates into O2 molecules and O atoms: O3 + hν → O2 + O. A 1.00 L sample of air at 22 °C and 748 mmHg contains 0.25 ppm of O3. How much energy, in joules, must be absorbed if O3 all the molecules in the sample of air are to dissociate? Assume
Radio signals from Voyager 1 in the 1970s were broadcast at a frequency of 8.4 GHz. On Earth, this radiation was received by an antenna able to detect signals as weak as 4 x 10-21 W. How many photons per second does this detection limit represent?
Certain metal compounds impart colors to flames—sodium compounds, yellow; lithium, red; barium, green—and flame tests can be used to detect these elements. (a) At a flame temperature of 800 °C, can collisions between gaseous atoms with average kinetic energies supply the energies required for
The angular momentum of an electron in the Bohr hydrogen atom is mur, where m is the mass of the electron, u, its velocity, and r, the radius of the Bohr orbit. The angular momentum can have only the values nh/2π, where n is an integer (the number of the Bohr orbit). Show that the circumferences
A molecule of chlorine can be dissociated into atoms by absorbing a photon of sufficiently high energy. Any excess energy is translated into kinetic energy as the atoms recoil from one another. If a molecule of chlorine at rest absorbs a photon of 300 nm wavelength, what will be the velocity of the
Using the relationships given in Table 8.2, find the finite values of r, in terms of a0, of the nodes for a 3s orbital.Table 8.2 TABLE 8.2 The Angular and Radial Parts of the Wave Functions for a Hydrogen-Like Atom Angular Part Y(0, 6) Radial Part
Refer to the Integrative Example. Determine whether or not n = 138 is a bound state. If it is, what sort of state is it? What is the radius of the orbit and how many revolutions per second does the electron make about the nucleus?
Using the relationships in Table 8.2, prepare a sketch of the 95% probability surface of a 4px orbital.Table 8.2 TABLE 8.2 The Angular and Radial Parts of the Wave Functions for a Hydrogen-Like Atom Angular Part Y(0, 6) Radial Part
Use a graphical method or some other means to determine the radius at which the probability of finding a 2s orbital is maximum.
Given that the volume of a sphere is V = (4/3)πr3, show that the volume, dV, of a thin spherical shell of radius r and thickness dr is 4πr2dr.
In the ground state of a hydrogen atom, what is the probability of finding an electron anywhere in a sphere of radius (a) a0, or (b) 2a0?
When atoms in excited states collide with unexcited atoms they can transfer their excitation energy to those atoms. The most efficient energy transfer occurs when the excitation energy matches the energy of an excited state in the unexcited atom. Assuming that we have a collection of excited
We have noted that an emission spectrum is a kind of “atomic fingerprint.” The various steels are alloys of iron and carbon, usually containing one or more other metals. Based on the principal lines of their atomic spectra, which of the metals in the table above are likely to be present in a
Balmer seems to have deduced his formula for the visible spectrum of hydrogen just by manipulating numbers. A more common scientific procedure is to graph experimental data and then find a mathematical equation to describe the graph. Show that equation (8.4) describes a straight line. Indicate
Emission and absorption spectra of the hydrogen atom exhibit line spectra characteristic of quantized systems. In an absorption experiment, a sample of hydrogen atoms is irradiated with light with wavelengths ranging from 100 to 1000 nm. In an emission spectrum experiment, the hydrogen atoms are
The emission spectrum below is for hydrogen atoms in the gas phase. The spectrum is of the first few emission lines from principal quantum number 6 down to all possible lower levels.As discussed in Are You Wondering 8-6, not all possible de-excitations are possible; the transitions are governed by
Diffraction of radiation takes place when the distance between the scattering centers is comparable to the wavelength of the radiation.(a) What velocity must helium atoms possess to be diffracted by a film of silver atoms in which the spacing is 100 pm?(b) Electrons accelerated through a certain
In your own words, define the following terms or symbols: (a) λ;(b) ν;(c) h; (d) ψ(e) principal quantum number, n.
Briefly describe each of the following ideas or phenomena:(a) Atomic (line) spectrum; (b) Photoelectric effect; (c) Matter wave; (d) Heisenberg uncertainty principle; (e) Electron spin; (f) Pauli exclusion principle;(g) Hund’s rule; (h) Orbital diagram; (i) Electron charge density; (j)

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