Estimate the minimum kinetic energy an object of mass, m, would have if it were localized in space to within a certain radius from a reference point? Give a numerical estimate for each of the following cases: a) A1 gram mass of copper localized to a spherical region of radius of 10-3cm. b) The center of mass of the Earth (mass = 6 x 1024kg) localized to a spherical region of radius of 1 m. c) A proton (mass of about 1.7 x 10-27kg) localized to a spherical region of 1 atomic radius (x 10-8cm). d) An electron (mass of about 9 x 10-31kg) localized to a spherical region of 1 atomic radius (x 10-8cm). For all parts, express the answer in terms of Joules, but in addition, express the answers in electron volts for parts c and d. Note that h = 6.626 × 10-34Js and 1eV = 1.6 x 10-19J. Hints: Use the Heisenberg uncertainty principle. Make use of the fact that it involves standard deviations in
Estimate the minimum kinetic energy an object of mass, m, would have if it were localized in space to within a certain radius from a reference point? Give a numerical estimate for each of the following cases: a) A1 gram mass of copper localized to a spherical region of radius of 10-3cm. b) The center of mass of the Earth (mass = 6 x 1024kg) localized to a spherical region of radius of 1 m. c) A proton (mass of about 1.7 x 10-27kg) localized to a spherical region of 1 atomic radius (x 10-8cm). d) An electron (mass of about 9 x 10-31kg) localized to a spherical region of 1 atomic radius (x 10-8cm). For all parts, express the answer in terms of Joules, but in addition, express the answers in electron volts for parts c and d. Note that h = 6.626 × 10-34Js and 1eV = 1.6 x 10-19J. Hints: Use the Heisenberg uncertainty principle. Make use of the fact that it involves standard deviations in
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Transcribed Image Text:Estimate the minimum kinetic energy an object of mass, m,
would have if it were localized in space to within a certain radius from a reference point? Give a numerical
estimate for each of the following cases:
a) A1 gram mass of copper localized to a spherical region of radius of 10-3cm.
b) The center of mass of the Earth (mass 6 × 1024kg) localized to a spherical region of radius of 1 m.
c) A proton (mass of about 1.7 × 10-27kg) localized to a spherical region of 1 atomic radius ( 10-8cm).
d) An electron (mass of about 9 x 10-31kg) localized to a spherical region of 1 atomic radius (x 10-8cm).
For all parts, express the answer in terms of Joules, but in addition, express the answers in electron volts for
parts c and d. Note that h = 6.626 × 10-34Js and leV = 1.6 x 10-19.
Hints: Use the Heisenberg uncertainty principle. Make use of the fact that it involves standard deviations in
momentum and position. Use the information given to estimate these standard deviations for each of the
cases. Then relate kinetic energy to this information (somehow).
(e) Explain how kinetic energy can be related to the uncertainty in various quantities. Some logic is required
to make this connection, and you need to provide the rationale to get credit for this part.
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