Concept explainers
An official baseball has a mass of
(a) Assuming that a baseball in New Orlean’s Superdome (width
(b) Assuming that the energy in part a is all kinetic energy
(c) A hit baseball can travel as fast as
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Physical Chemistry
- Consider burning ethane gas, C2H6 in oxygen (combustion) forming CO2 and water. (a) How much energy (in J) is produced in the combustion of one molecule of ethane? (b) What is the energy of a photon of ultraviolet light with a wavelength of 12.6 nm? (c) Compare your answers for (a) and (b).arrow_forwardWhat experimental evidence supports the quantum theory of light? Explain the wave-particle duality of all matter .. For what size particles must one consider both the wave and the particle properties?arrow_forward• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.arrow_forward
- (a) For n = 4, what are the possible values of l? (b) For l = 2,what are the possible values of ml? (c) If ml is 2, what are thepossible values for l?arrow_forward(a) If the kinetic energy of an electron is known to liebetween 1.59 × 10-19 J and 1.61 × 10-19 J, what is thesmallest distance within which it can be known to lie?(b) Repeat the calculation of part (a) for a helium atominstead of an electron.arrow_forwardThe radial wave function of a quantum state of Hydrogen is given by R(r)= (1/[4(2π)^{1/2}])a^{-3/2}( 2 - r/a ) exp(-r/2a), where a is the Bohr radius. (a) Show analytically that this function has an extremum at r=4a. (b) Sketch the graph of R(r) x r. For a decent sketch of this graph, take into account some values of R(r) at certain points of interest, such as r=0, 2a, 4a, and so on. Also take into account the extremes of the function R(r) and their inflection points, as well as the limit r--> infinity. (c) Determine the radial probability density P(r) associated with the quantum state in question. (d) Show that the function P(r) you determined in part (c) is properly normalized.arrow_forward
- P7D.8* A particle is confined to move in a one-dimensional box of length L. If the particle is behaving classically, then it simply bounces back and forth in the box, moving with a constant speed. (a) Explain why the probability density, P(x), for the classical particle is 1/L. (Hint: What is the total probability of finding the particle in the box?) (b) Explain why the average value of x" is (x")= , P(x)x"dx . (c) By evaluating such an integral, find (x) and (x*). (d) For a quantum particle (x)=L/2 and (x*)=L (}-1/2n°n²). Compare these expressions with those you have obtained in (c), recalling that the correspondence principle states that, for very large values of the quantum numbers, the predictions of quantum mechanics approach those of classical mechanics.arrow_forwardW 4. (a) A laser emits light that has a frequency of 4.69 X 10¹4 s¹. What is the energy of one photon of this radiation? V (b) If the laser emits a pulse containing 5.0 X 1017 photons of this radiation, what is the total energy of that pulse? (c) If the laser emits 1.3 X 10-2 J of energy during a pulse, how many photons are emitted?arrow_forward(a) For a particle in the stationary state n of a one dimensional box of length a, find the probability that the particle is in the region 0xa/4.(b) Calculate this probability for n=1,2, and 3.arrow_forward
- What is the orbital angular momentum (as multiples of h) of an electron in the orbitals (a) 1s. (b) 3s. (c) 3d. (d) 2p. (e) 3p? Give the numbers of angular and radial nodes in each case.arrow_forwardIn each of the following cases, demonstrate that 2n² is the number of sets of quantum numbers (e, me, m) possible for a hydrogen atom in the n-th shell. In each case, accomplish this by specifying the number of states in each subshell. Submit the numbers for all subshells, separated by spaces, in the single answer box for each case. (a) n = 1 2 (b) n = 2 122 (c) n = 3 242 (d) n = 4 362 (e) n = 5 482 Need Help? X X X X Read Itarrow_forwardThe work function of metal is the minimum energy required to produce photoelectric effect on that metal, and the work function for potassium metal is 2.30 eV (where 1 eV = 1.60 x 10–19 J).(a) What is the minimum energy in Joules required to eject an electron from potassium metal?(b) What is the longest wavelength of light, in nanometers (nm), capable of producing photoelectric effect on potassium metal? (c) Determine whether a photon of green light with = 512 nm would have sufficient energy to eject an electron from a potassium metal. (d) If an electron is ejected, determine the kinetic energy and the speed of the ejected electron, which has a mass of 9.11 x 10–31 kg. .(Planck’s constant, h = 6.626 x 10–34 J∙s.; speed of light, c = 3.00 x 108 m/s; 1 J = 1 kg∙m2/s2)arrow_forward
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