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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_forwardCalculate the momentum of an X-ray photon with a wavelength of 0.17nm. How does this value compare with the momentum of a free electron that has been accelerated through a potential difference of 5000 volts? (Hint: electron mass, m, = 9.10938 x 10" kg; electron charge e = 1.602 x 10"C; speed of light e = 3.0 x 10° m.s'; 1.00 J= 1.00 VC; h = 6.626 x 10"J.s. The various energy units are: 1 J=1 kg.m's", 1.00 cV =1VC, leV = 1.602 x 10"J, 1J=6.242 x 10" eV, etc.). %3D %3Darrow_forward106. Combining two real wave functions ₁ and 2, the following functions are constructed: A = ₁ + $₂₂ B = = ₁ +i0₂, C = ₁ −i0₂, D=i(0₁ +0₂). The correct statement will then be (a) A and B represent the same state (c) A and D represents the same state (b) A and C represent the same state. (d) B and D represent the same state.arrow_forward
- Calculate the momentum of an X-ray photon with a wavelength of 0.17nm. How does this value compare with the momentum of a free electron that has been accelerated through a potential difference of 5000 volts? (Hint: electron mass, m, = 9.10938 x 10" kg; electron charge e = 1.602 x 10"C; speed of light e = 3.0 x 10* m.s'; 1.00 J= 1.00 VC; h = 6.626 x 10"J.s. The various energy units are: 1 J= 1 kg.m°s³, 1.00 eV =1VC, leV= 1.602 x 10"J, 1J= 6.242 x 10" eV, etc.). %3Darrow_forwardA hydrogen atom consists of a proton and an electron. According to the Bohr theory, the electron revolves about the proton in a circle of radius a (a = 5 · 10−9cm for the ground state). According to quantum mechanics, the electron may be at any distance r (from 0 to ∞) from the proton; for the ground state, the probability that the electron is in a volume element dV , at a distance r to r + dr from the proton, is proportional to e−2r/adV , where a is the Bohr radius. Write dV in spherical coordinates (see Chapter 5, Section 4) and find the density function f(r) so that f(r) dr is the probability that the electron is at a distance between r and r + drfrom the proton. (Remember that the probability for the electron to be somewhere must be 1.) Computer plot f(r) and show that its maximum value is at r = a; we then say that the most probable value of r is a. Also show that the average value of r−1 is a−1.arrow_forwardDetermine the value of x if -84.2 = ln(1.34e+4)xarrow_forward
- The 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_forwardExplain the physical significance of a negative for delta E. Why must E photon always be positive, while delta E can be negative or positive?arrow_forwardCalculate the energy of a photon of light (in Joules) with a wavelength of (5.40x10^2) nm. Use a value of (3.000x10^8) for the speed of light. Remember 1 m = (1.0000x10^9) nm h = (6.626x10^-34) Js Do not include units with your answer. Note: Your answer is assumed to be reduced to the highest power possible. Your Answer: x10 Answerarrow_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_forwardThe speed of a certain proton is 0.45 Mm 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?arrow_forwardSuppose that the microwave radiation has a wavelength of 12.4 cm. How many photons are required to heat 285 mL of coffee from 25.0 ∘C∘C to 62.0 ∘C∘C? Assume that the coffee has the same density, 0.997 g mL−1, and specific heat capacity, 4.184 J g−1 K−1, as water over this temperature range. Express the number of photons numerically.arrow_forward
- Chemistry: Principles and ReactionsChemistryISBN:9781305079373Author:William L. Masterton, Cecile N. HurleyPublisher:Cengage LearningChemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage Learning