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4. A scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of 0.12 nm and its momentum along this axis with a standard deviation of 3.0 x1025 kg-m/s. Use the Heisenberg uncertainty principle to evaluate the validity of this claim.

4. A scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of 0.12 nm and its momentum along this axis with a standard deviation of 3.0 x1025 kg-m/s. Use the Heisenberg uncertainty principle to evaluate the validity of this claim.

Chemistry
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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1. In an experiment to study the photoelectric effect, a scientist measures the kinetic energy of ejected electrons as a function of the frequency of radiation hitting a metal surface. She obtains the following plot. The point labelled "vo" corresponds to light with a wavelength of 680 nm. Frequency a. What is the value of vo in s-1? b. What is the value of the work function of the metal in J? c. What happens when the metal is irradiated with light of frequency less than vo? d. Note that when the frequency of the light is greater than vo, the plot shows a straight line with a nonzero slope. Why is this the case? e. Can you determine the slope of the line segment discussed in part (d)? Explain. 2. An electron starting from rest, accelerates through a potential difference of 418 V. What is the final de Broglie wavelength of the electron, assuming that its final speed is much less than the speed of light? 3. In the Bohr model of the hydrogen atom, what is the de Broglie wavelength for the electron when it is in (a) n = 1 level and (b) n = 4 level? In each case, compare the de Broglie wavelength to the circumference 2Tr, of the orbit. 4. A scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of 0.12 nm and its momentum along this axis with a standard deviation of 3.0 x1025 kg-m/s. Use the Heisenberg uncertainty principle to evaluate the validity of this claim. 5. The Schrödinger equation for a particle of mass m that is constrained to move freely along a line between 0 and a is (8n²mE` W(x) = 0 dx2 with the boundary condition y(0) = p(a) = 0 In this equation, E is the energy of the particle and (x) is its wave function. Solve this differential equation for (x), and apply the boundary conditions. Electron o kinetic energy
Transcribed Image Text:1. In an experiment to study the photoelectric effect, a scientist measures the kinetic energy of ejected electrons as a function of the frequency of radiation hitting a metal surface. She obtains the following plot. The point labelled "vo" corresponds to light with a wavelength of 680 nm. Frequency a. What is the value of vo in s-1? b. What is the value of the work function of the metal in J? c. What happens when the metal is irradiated with light of frequency less than vo? d. Note that when the frequency of the light is greater than vo, the plot shows a straight line with a nonzero slope. Why is this the case? e. Can you determine the slope of the line segment discussed in part (d)? Explain. 2. An electron starting from rest, accelerates through a potential difference of 418 V. What is the final de Broglie wavelength of the electron, assuming that its final speed is much less than the speed of light? 3. In the Bohr model of the hydrogen atom, what is the de Broglie wavelength for the electron when it is in (a) n = 1 level and (b) n = 4 level? In each case, compare the de Broglie wavelength to the circumference 2Tr, of the orbit. 4. A scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultaneously the position of a particle along an axis with a standard deviation of 0.12 nm and its momentum along this axis with a standard deviation of 3.0 x1025 kg-m/s. Use the Heisenberg uncertainty principle to evaluate the validity of this claim. 5. The Schrödinger equation for a particle of mass m that is constrained to move freely along a line between 0 and a is (8n²mE` W(x) = 0 dx2 with the boundary condition y(0) = p(a) = 0 In this equation, E is the energy of the particle and (x) is its wave function. Solve this differential equation for (x), and apply the boundary conditions. Electron o kinetic energy
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