[{"problem_text": "Radiation from an X-ray source consists of two components of wavelengths $154.433 \\mathrm{pm}$ and $154.051 \\mathrm{pm}$. Calculate the difference in glancing angles $(2 \\theta)$ of the diffraction lines arising from the two components in a diffraction pattern from planes of separation $77.8 \\mathrm{pm}$.", "answer_latex": " 2.14", "answer_number": "2.14", "unit": " ${\\circ}$", "source": "matter", "problemid": " 37.7(a)", "comment": " ", "solution": ""}, {"problem_text": "A chemical reaction takes place in a container of cross-sectional area $50 \\mathrm{~cm}^2$. As a result of the reaction, a piston is pushed out through $15 \\mathrm{~cm}$ against an external pressure of $1.0 \\mathrm{~atm}$. Calculate the work done by the system.", "answer_latex": " -75", "answer_number": "-75", "unit": " $\\mathrm{~J}$", "source": "matter", "problemid": " 55.4(a)", "comment": " ", "solution": ""}, {"problem_text": "A mixture of water and ethanol is prepared with a mole fraction of water of 0.60 . If a small change in the mixture composition results in an increase in the chemical potential of water by $0.25 \\mathrm{~J} \\mathrm{~mol}^{-1}$, by how much will the chemical potential of ethanol change?", "answer_latex": " -0.38", "answer_number": "-0.38", "unit": " $\\mathrm{~J} \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 69.2(a)", "comment": " ", "solution": ""}, {"problem_text": "The enthalpy of fusion of mercury is $2.292 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$, and its normal freezing point is $234.3 \\mathrm{~K}$ with a change in molar volume of $+0.517 \\mathrm{~cm}^3 \\mathrm{~mol}^{-1}$ on melting. At what temperature will the bottom of a column of mercury (density $13.6 \\mathrm{~g} \\mathrm{~cm}^{-3}$ ) of height $10.0 \\mathrm{~m}$ be expected to freeze?", "answer_latex": " 234.4", "answer_number": "234.4", "unit": " $ \\mathrm{~K}$ ", "source": "matter", "problemid": " 69.3", "comment": " problem", "solution": ""}, {"problem_text": "Suppose a nanostructure is modelled by an electron confined to a rectangular region with sides of lengths $L_1=1.0 \\mathrm{~nm}$ and $L_2=2.0 \\mathrm{~nm}$ and is subjected to thermal motion with a typical energy equal to $k T$, where $k$ is Boltzmann's constant. How low should the temperature be for the thermal energy to be comparable to the zero-point energy\uff1f", "answer_latex": " 5.5", "answer_number": "5.5", "unit": " $10^3 \\mathrm{~K}$", "source": "matter", "problemid": " 11.3(a)", "comment": " ", "solution": ""}, {"problem_text": "Calculate the change in Gibbs energy of $35 \\mathrm{~g}$ of ethanol (mass density $0.789 \\mathrm{~g} \\mathrm{~cm}^{-3}$ ) when the pressure is increased isothermally from 1 atm to 3000 atm.", "answer_latex": " 12", "answer_number": "12", "unit": " $\\mathrm{~kJ}$", "source": "matter", "problemid": " 66.5(a)", "comment": " ", "solution": ""}, {"problem_text": "The promotion of an electron from the valence band into the conduction band in pure $\\mathrm{TIO}_2$ by light absorption requires a wavelength of less than $350 \\mathrm{~nm}$. Calculate the energy gap in electronvolts between the valence and conduction bands.", "answer_latex": " 3.54", "answer_number": "3.54", "unit": " $\\mathrm{eV}$", "source": "matter", "problemid": " 39.1(a)", "comment": " ", "solution": ""}, {"problem_text": "Although the crystallization of large biological molecules may not be as readily accomplished as that of small molecules, their crystal lattices are no different. Tobacco seed globulin forms face-centred cubic crystals with unit cell dimension of $12.3 \\mathrm{~nm}$ and a density of $1.287 \\mathrm{~g} \\mathrm{~cm}^{-3}$. Determine its molar mass.", "answer_latex": "3.61", "answer_number": "3.61", "unit": " $10^5 \\mathrm{~g} \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 37.1", "comment": " problem", "solution": ""}, {"problem_text": "An electron is accelerated in an electron microscope from rest through a potential difference $\\Delta \\phi=100 \\mathrm{kV}$ and acquires an energy of $e \\Delta \\phi$. What is its final speed?", "answer_latex": " 1.88", "answer_number": "1.88", "unit": " $10^8 \\mathrm{~m} \\mathrm{~s}^{-1}$", "source": "matter", "problemid": " 2.7(a)", "comment": " ", "solution": ""}, {"problem_text": "The following data show how the standard molar constant-pressure heat capacity of sulfur dioxide varies with temperature. By how much does the standard molar enthalpy of $\\mathrm{SO}_2(\\mathrm{~g})$ increase when the temperature is raised from $298.15 \\mathrm{~K}$ to $1500 \\mathrm{~K}$ ?", "answer_latex": " 62.2", "answer_number": "62.2", "unit": " $\\mathrm{~kJ} \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 56.1", "comment": " problem", "solution": ""}, {"problem_text": "Suppose that the normalized wavefunction for an electron in a carbon nanotube of length $L=10.0 \\mathrm{~nm}$ is: $\\psi=(2 / L)^{1 / 2} \\sin (\\pi x / L)$. Calculate the probability that the electron is between $x=4.95 \\mathrm{~nm}$ and $5.05 \\mathrm{~nm}$.", "answer_latex": " 0.020", "answer_number": "0.020", "unit": " ", "source": "matter", "problemid": " 5.1(a)", "comment": " problem", "solution": ""}, {"problem_text": "A sample of the sugar D-ribose of mass $0.727 \\mathrm{~g}$ was placed in a calorimeter and then ignited in the presence of excess oxygen. The temperature rose by $0.910 \\mathrm{~K}$. In a separate experiment in the same calorimeter, the combustion of $0.825 \\mathrm{~g}$ of benzoic acid, for which the internal energy of combustion is $-3251 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$, gave a temperature rise of $1.940 \\mathrm{~K}$. Calculate the enthalpy of formation of D-ribose.", "answer_latex": " -1270", "answer_number": "-1270", "unit": " $\\mathrm{~kJ} \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 57.1", "comment": " problem", "solution": ""}, {"problem_text": "An electron confined to a metallic nanoparticle is modelled as a particle in a one-dimensional box of length $L$. If the electron is in the state $n=1$, calculate the probability of finding it in the following regions: $0 \\leq x \\leq \\frac{1}{2} L$.", "answer_latex": " $\\frac{1}{2}$", "answer_number": "0.5", "unit": " ", "source": "matter", "problemid": " 9.3(a)", "comment": " problem", "solution": ""}, {"problem_text": "The carbon-carbon bond length in diamond is $154.45 \\mathrm{pm}$. If diamond were considered to be a close-packed structure of hard spheres with radii equal to half the bond length, what would be its expected density? The diamond lattice is face-centred cubic and its actual density is $3.516 \\mathrm{~g} \\mathrm{~cm}^{-3}$.", "answer_latex": " 7.654", "answer_number": "7.654", "unit": " $\\mathrm{~g} \\mathrm{~cm}^{-3}$", "source": "matter", "problemid": " 38.3", "comment": " problem", "solution": ""}, {"problem_text": "A swimmer enters a gloomier world (in one sense) on diving to greater depths. Given that the mean molar absorption coefficient of seawater in the visible region is $6.2 \\times 10^{-3} \\mathrm{dm}^3 \\mathrm{~mol}^{-1} \\mathrm{~cm}^{-1}$, calculate the depth at which a diver will experience half the surface intensity of light.", "answer_latex": " 0.87", "answer_number": "0.87", "unit": " $\\mathrm{~m}$", "source": "matter", "problemid": " 40.7(a)", "comment": " ", "solution": ""}, {"problem_text": "Calculate the molar energy required to reverse the direction of an $\\mathrm{H}_2 \\mathrm{O}$ molecule located $100 \\mathrm{pm}$ from a $\\mathrm{Li}^{+}$ ion. Take the magnitude of the dipole moment of water as $1.85 \\mathrm{D}$.", "answer_latex": " 1.07", "answer_number": "1.07", "unit": " $10^3 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 35.1(a)", "comment": " ", "solution": ""}, {"problem_text": "In an industrial process, nitrogen is heated to $500 \\mathrm{~K}$ at a constant volume of $1.000 \\mathrm{~m}^3$. The gas enters the container at $300 \\mathrm{~K}$ and $100 \\mathrm{~atm}$. The mass of the gas is $92.4 \\mathrm{~kg}$. Use the van der Waals equation to determine the approximate pressure of the gas at its working temperature of $500 \\mathrm{~K}$. For nitrogen, $a=1.39 \\mathrm{dm}^6 \\mathrm{~atm} \\mathrm{~mol}^{-2}, b=0.0391 \\mathrm{dm}^3 \\mathrm{~mol}^{-1}$.", "answer_latex": " 140", "answer_number": "140", "unit": " $\\mathrm{~atm}$", "source": "matter", "problemid": " 36.6(a)", "comment": " ", "solution": ""}, {"problem_text": "The chemical shift of the $\\mathrm{CH}_3$ protons in acetaldehyde (ethanal) is $\\delta=2.20$ and that of the $\\mathrm{CHO}$ proton is 9.80 . What is the difference in local magnetic field between the two regions of the molecule when the applied field is $1.5 \\mathrm{~T}$", "answer_latex": " 11", "answer_number": "11", "unit": " $\\mu \\mathrm{T}$", "source": "matter", "problemid": " 48.2(a)", "comment": " ", "solution": ""}, {"problem_text": "Suppose that the junction between two semiconductors can be represented by a barrier of height $2.0 \\mathrm{eV}$ and length $100 \\mathrm{pm}$. Calculate the transmission probability of an electron with energy $1.5 \\mathrm{eV}$.", "answer_latex": " 0.8", "answer_number": "0.8", "unit": " ", "source": "matter", "problemid": " 10.1(a)", "comment": " ", "solution": ""}, {"problem_text": "The diffusion coefficient of a particular kind of t-RNA molecule is $D=1.0 \\times 10^{-11} \\mathrm{~m}^2 \\mathrm{~s}^{-1}$ in the medium of a cell interior. How long does it take molecules produced in the cell nucleus to reach the walls of the cell at a distance $1.0 \\mu \\mathrm{m}$, corresponding to the radius of the cell?", "answer_latex": " 1.7", "answer_number": "1.7", "unit": " $10^{-2} \\mathrm{~s}$", "source": "matter", "problemid": " 81.11", "comment": " problem", "solution": ""}, {"problem_text": "At what pressure does the mean free path of argon at $20^{\\circ} \\mathrm{C}$ become comparable to the diameter of a $100 \\mathrm{~cm}^3$ vessel that contains it? Take $\\sigma=0.36 \\mathrm{~nm}^2$", "answer_latex": " 0.195", "answer_number": "0.195", "unit": " $\\mathrm{Pa}$", "source": "matter", "problemid": " 78.6(a)", "comment": " ", "solution": ""}, {"problem_text": "The equilibrium pressure of $\\mathrm{O}_2$ over solid silver and silver oxide, $\\mathrm{Ag}_2 \\mathrm{O}$, at $298 \\mathrm{~K}$ is $11.85 \\mathrm{~Pa}$. Calculate the standard Gibbs energy of formation of $\\mathrm{Ag}_2 \\mathrm{O}(\\mathrm{s})$ at $298 \\mathrm{~K}$.", "answer_latex": " -11.2", "answer_number": "-11.2", "unit": " $\\mathrm{~kJ}   \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 73.4(a)", "comment": " ", "solution": ""}, {"problem_text": "When alkali metals dissolve in liquid ammonia, their atoms each lose an electron and give rise to a deep-blue solution that contains unpaired electrons occupying cavities in the solvent. These 'metal-ammonia solutions' have a maximum absorption at $1500 \\mathrm{~nm}$. Supposing that the absorption is due to the excitation of an electron in a spherical square well from its ground state to the next-higher state (see the preceding problem for information), what is the radius of the cavity?", "answer_latex": " 0.69", "answer_number": "0.69", "unit": " $\\mathrm{~nm}$", "source": "matter", "problemid": " 11.5", "comment": " problem", "solution": ""}, {"problem_text": "Electron diffraction makes use of electrons with wavelengths comparable to bond lengths. To what speed must an electron be accelerated for it to have a wavelength of $100 \\mathrm{pm}$ ? ", "answer_latex": " 7.27", "answer_number": "7.27", "unit": " $10^6 \\mathrm{~m} \\mathrm{~s}^{-1}$", "source": "matter", "problemid": " 4.8(a)", "comment": " ", "solution": ""}, {"problem_text": "Nelson, et al. (Science 238, 1670 (1987)) examined several weakly bound gas-phase complexes of ammonia in search of examples in which the $\\mathrm{H}$ atoms in $\\mathrm{NH}_3$ formed hydrogen bonds, but found none. For example, they found that the complex of $\\mathrm{NH}_3$ and $\\mathrm{CO}_2$ has the carbon atom nearest the nitrogen (299 pm away): the $\\mathrm{CO}_2$ molecule is at right angles to the $\\mathrm{C}-\\mathrm{N}$ 'bond', and the $\\mathrm{H}$ atoms of $\\mathrm{NH}_3$ are pointing away from the $\\mathrm{CO}_2$. The magnitude of the permanent dipole moment of this complex is reported as $1.77 \\mathrm{D}$. If the $\\mathrm{N}$ and $\\mathrm{C}$ atoms are the centres of the negative and positive charge distributions, respectively, what is the magnitude of those partial charges (as multiples of $e$ )?", "answer_latex": " 0.123", "answer_number": "0.123", "unit": " ", "source": "matter", "problemid": " 34.5", "comment": " problem", "solution": ""}, {"problem_text": "The NOF molecule is an asymmetric rotor with rotational constants $3.1752 \\mathrm{~cm}^{-1}, 0.3951 \\mathrm{~cm}^{-1}$, and $0.3505 \\mathrm{~cm}^{-1}$. Calculate the rotational partition function of the molecule at $25^{\\circ} \\mathrm{C}$.", "answer_latex": " 7.97", "answer_number": "7.97", "unit": "$10^3$", "source": "matter", "problemid": " 52.4(a)", "comment": " ", "solution": ""}, {"problem_text": "Suppose that $2.5 \\mathrm{mmol} \\mathrm{N}_2$ (g) occupies $42 \\mathrm{~cm}^3$ at $300 \\mathrm{~K}$ and expands isothermally to $600 \\mathrm{~cm}^3$. Calculate $\\Delta G$ for the process.", "answer_latex": " -17", "answer_number": "-17", "unit": " $\\mathrm{~J}$ ", "source": "matter", "problemid": " 66.1(a)", "comment": " ", "solution": ""}, {"problem_text": "Calculate the standard potential of the $\\mathrm{Ce}^{4+} / \\mathrm{Ce}$ couple from the values for the $\\mathrm{Ce}^{3+} / \\mathrm{Ce}$ and $\\mathrm{Ce}^{4+} / \\mathrm{Ce}^{3+}$ couples.\r\n", "answer_latex": " -1.46", "answer_number": "-1.46", "unit": " $\\mathrm{V}$", "source": "matter", "problemid": " 77.1(a)", "comment": " ", "solution": ""}, {"problem_text": "An effusion cell has a circular hole of diameter $1.50 \\mathrm{~mm}$. If the molar mass of the solid in the cell is $300 \\mathrm{~g} \\mathrm{~mol}^{-1}$ and its vapour pressure is $0.735 \\mathrm{~Pa}$ at $500 \\mathrm{~K}$, by how much will the mass of the solid decrease in a period of $1.00 \\mathrm{~h}$ ?", "answer_latex": " 16", "answer_number": "16", "unit": " $\\mathrm{mg}$", "source": "matter", "problemid": " 78.11(a)", "comment": " ", "solution": ""}, {"problem_text": "The speed of a certain proton is $6.1 \\times 10^6 \\mathrm{~m} \\mathrm{~s}^{-1}$. If the uncertainty in its momentum is to be reduced to 0.0100 per cent, what uncertainty in its location must be tolerated?", "answer_latex": " 52", "answer_number": "52", "unit": " $\\mathrm{pm}$", "source": "matter", "problemid": " 8.1(a)", "comment": " ", "solution": ""}, {"problem_text": "It is possible to produce very high magnetic fields over small volumes by special techniques. What would be the resonance frequency of an electron spin in an organic radical in a field of $1.0 \\mathrm{kT}$ ?", "answer_latex": " 2.8", "answer_number": "2.8", "unit": " $10^{13} \\mathrm{~Hz}$", "source": "matter", "problemid": " 50.1", "comment": " problem", "solution": ""}, {"problem_text": "A particle of mass $1.0 \\mathrm{~g}$ is released near the surface of the Earth, where the acceleration of free fall is $g=8.91 \\mathrm{~m} \\mathrm{~s}^{-2}$. What will be its kinetic energy after  $1.0 \\mathrm{~s}$. Ignore air resistance?", "answer_latex": "48", "answer_number": "48", "unit": " $\\mathrm{~mJ}$", "source": "matter", "problemid": " 2.1(a)", "comment": " ", "solution": ""}, {"problem_text": "The flux of visible photons reaching Earth from the North Star is about $4 \\times 10^3 \\mathrm{~mm}^{-2} \\mathrm{~s}^{-1}$. Of these photons, 30 per cent are absorbed or scattered by the atmosphere and 25 per cent of the surviving photons are scattered by the surface of the cornea of the eye. A further 9 per cent are absorbed inside the cornea. The area of the pupil at night is about $40 \\mathrm{~mm}^2$ and the response time of the eye is about $0.1 \\mathrm{~s}$. Of the photons passing through the pupil, about 43 per cent are absorbed in the ocular medium. How many photons from the North Star are focused onto the retina in $0.1 \\mathrm{~s}$ ?", "answer_latex": " 4.4", "answer_number": "4.4", "unit": " $10^3$", "source": "matter", "problemid": " 40.3", "comment": " problem", "solution": ""}, {"problem_text": "When ultraviolet radiation of wavelength $58.4 \\mathrm{~nm}$ from a helium lamp is directed on to a sample of krypton, electrons are ejected with a speed of $1.59 \\times 10^6 \\mathrm{~m} \\mathrm{~s}^{-1}$. Calculate the ionization energy of krypton.\r\n", "answer_latex": " 14", "answer_number": "14", "unit": " $\\mathrm{eV}$", "source": "matter", "problemid": " 17.2(a)", "comment": " ", "solution": ""}, {"problem_text": " If $125 \\mathrm{~cm}^3$ of hydrogen gas effuses through a small hole in 135 seconds, how long will it take the same volume of oxygen gas to effuse under the same temperature and pressure?", "answer_latex": " 537", "answer_number": "537", "unit": " $\\mathrm{s}$", "source": "matter", "problemid": " 78.10(a)", "comment": " ", "solution": ""}, {"problem_text": "The vibrational wavenumber of $\\mathrm{Br}_2$ is $323.2 \\mathrm{~cm}^{-1}$. By evaluating the vibrational partition function explicitly (without approximation), at what temperature is the value within 5 per cent of the value calculated from the approximate formula?", "answer_latex": " 4500", "answer_number": "4500", "unit": "$\\mathrm{~K}$", "source": "matter", "problemid": " 52.10(a)", "comment": " ", "solution": ""}, {"problem_text": "A thermodynamic study of $\\mathrm{DyCl}_3$ (E.H.P. Cordfunke, et al., J. Chem. Thermodynamics 28, 1387 (1996)) determined its standard enthalpy of formation from the following information\r\n(1) $\\mathrm{DyCl}_3(\\mathrm{~s}) \\rightarrow \\mathrm{DyCl}_3(\\mathrm{aq}$, in $4.0 \\mathrm{M} \\mathrm{HCl}) \\quad \\Delta_{\\mathrm{r}} H^{\\ominus}=-180.06 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$\r\n(2) $\\mathrm{Dy}(\\mathrm{s})+3 \\mathrm{HCl}(\\mathrm{aq}, 4.0 \\mathrm{~m}) \\rightarrow \\mathrm{DyCl}_3(\\mathrm{aq}$, in $4.0 \\mathrm{M} \\mathrm{HCl}(\\mathrm{aq}))+\\frac{3}{2} \\mathrm{H}_2(\\mathrm{~g})$ $\\Delta_{\\mathrm{r}} H^{\\ominus}=-699.43 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$\r\n(3) $\\frac{1}{2} \\mathrm{H}_2(\\mathrm{~g})+\\frac{1}{2} \\mathrm{Cl}_2(\\mathrm{~g}) \\rightarrow \\mathrm{HCl}(\\mathrm{aq}, 4.0 \\mathrm{M}) \\quad \\Delta_{\\mathrm{r}} H^{\\ominus}=-158.31 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$\r\nDetermine $\\Delta_{\\mathrm{f}} H^{\\ominus}\\left(\\mathrm{DyCl}_3, \\mathrm{~s}\\right)$ from these data.", "answer_latex": " -994.3", "answer_number": "-994.3", "unit": " $\\mathrm{~kJ} \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 57.5", "comment": " problem", "solution": ""}, {"problem_text": "Calculate $\\Delta_{\\mathrm{r}} G^{\\ominus}(375 \\mathrm{~K})$ for the reaction $2 \\mathrm{CO}(\\mathrm{g})+\\mathrm{O}_2(\\mathrm{~g}) \\rightarrow 2 \\mathrm{CO}_2(\\mathrm{~g})$ from the values of $\\Delta_{\\mathrm{r}} G^{\\ominus}(298 \\mathrm{~K})$ : and $\\Delta_{\\mathrm{r}} H^{\\ominus}(298 \\mathrm{~K})$, and the GibbsHelmholtz equation.", "answer_latex": "-501", "answer_number": "-501", "unit": "$\\mathrm{~kJ} \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 66.1", "comment": " problem", "solution": ""}, {"problem_text": "The vapour pressure of benzene is $53.3 \\mathrm{kPa}$ at $60.6^{\\circ} \\mathrm{C}$, but it fell to $51.5 \\mathrm{kPa}$ when $19.0 \\mathrm{~g}$ of an non-volatile organic compound was dissolved in $500 \\mathrm{~g}$ of benzene. Calculate the molar mass of the compound.", "answer_latex": " 85", "answer_number": "85", "unit": " $\\mathrm{~g} \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 70.8(a)", "comment": " ", "solution": ""}, {"problem_text": "J.G. Dojahn, et al. (J. Phys. Chem. 100, 9649 (1996)) characterized the potential energy curves of the ground and electronic states of homonuclear diatomic halogen anions. The ground state of $\\mathrm{F}_2^{-}$ is ${ }^2 \\sum_{\\mathrm{u}}^{+}$ with a fundamental vibrational wavenumber of $450.0 \\mathrm{~cm}^{-1}$ and equilibrium internuclear distance of $190.0 \\mathrm{pm}$. The first two excited states are at 1.609 and $1.702 \\mathrm{eV}$ above the ground state. Compute the standard molar entropy of $\\mathrm{F}_2^{-}$ at $ 298 \\mathrm{~K}$.", "answer_latex": " 199.4", "answer_number": "199.4", "unit": " $\\mathrm{~J} \\mathrm{~mol}^{-1} \\mathrm{~K}^{-1}$", "source": "matter", "problemid": " 60.3", "comment": " problem", "solution": ""}, {"problem_text": "The duration of a $90^{\\circ}$ or $180^{\\circ}$ pulse depends on the strength of the $\\mathscr{B}_1$ field. If a $180^{\\circ}$ pulse requires $12.5 \\mu \\mathrm{s}$, what is the strength of the $\\mathscr{B}_1$ field? ", "answer_latex": " 5.9", "answer_number": "5.9", "unit": " $10^{-4} \\mathrm{~T}$", "source": "matter", "problemid": " 49.1(a)", "comment": " ", "solution": ""}, {"problem_text": "In 1976 it was mistakenly believed that the first of the 'superheavy' elements had been discovered in a sample of mica. Its atomic number  was believed to be 126. What is the most probable distance of the innermost electrons from the nucleus of an atom of this element? (In such elements, relativistic effects are very important, but ignore them here.)", "answer_latex": " 0.42", "answer_number": "0.42", "unit": " $\\mathrm{pm}$", "source": "matter", "problemid": " 18.1", "comment": " problem", "solution": ""}, {"problem_text": "The ground level of $\\mathrm{Cl}$ is ${ }^2 \\mathrm{P}_{3 / 2}$ and a ${ }^2 \\mathrm{P}_{1 / 2}$ level lies $881 \\mathrm{~cm}^{-1}$ above it. Calculate the electronic contribution to the molar Gibbs energy of $\\mathrm{Cl}$ atoms at  $500 \\mathrm{~K}$.", "answer_latex": " -6.42", "answer_number": "-6.42", "unit": " $\\mathrm{~kJ} \\mathrm{~mol}^{-1}$", "source": "matter", "problemid": " 64.5(a)", "comment": " ", "solution": ""}, {"problem_text": "Calculate the melting point of ice under a pressure of 50 bar. Assume that the density of ice under these conditions is approximately $0.92 \\mathrm{~g} \\mathrm{~cm}^{-3}$ and that of liquid water is $1.00 \\mathrm{~g} \\mathrm{~cm}^{-3}$.", "answer_latex": " 272.8", "answer_number": "272.8", "unit": " $\\mathrm{K}$", "source": "matter", "problemid": " 69.9(a)", "comment": " ", "solution": ""}, {"problem_text": "What is the temperature of a two-level system of energy separation equivalent to $400 \\mathrm{~cm}^{-1}$ when the population of the upper state is one-third that of the lower state?", "answer_latex": " 524", "answer_number": "524", "unit": " $ \\mathrm{~K}$", "source": "matter", "problemid": " 51.4(a)", "comment": " ", "solution": ""}, {"problem_text": "At $300 \\mathrm{~K}$ and $20 \\mathrm{~atm}$, the compression factor of a gas is 0.86 . Calculate the volume occupied by $8.2 \\mathrm{mmol}$ of the gas under these conditions.", "answer_latex": " 8.7", "answer_number": "8.7", "unit": " $\\mathrm{~cm}^3$", "source": "matter", "problemid": " 36.3(a)", "comment": " problem", "solution": ""}, {"problem_text": "A very crude model of the buckminsterfullerene molecule $\\left(\\mathrm{C}_{60}\\right)$ is to treat it as a collection of electrons in a cube with sides of length equal to the mean diameter of the molecule $(0.7 \\mathrm{~nm})$. Suppose that only the $\\pi$ electrons of the carbon atoms contribute, and predict the wavelength of the first excitation of $\\mathrm{C}_{60}$. (The actual value is $730 \\mathrm{~nm}$.)", "answer_latex": " 1.6", "answer_number": "1.6", "unit": " $\\mu \\mathrm{m}$", "source": "matter", "problemid": " 11.3", "comment": " problem", "solution": ""}]