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Ive the following differential equations: а. dx2 - 4y = 0 y(0) = 2 (at x = 0) = 4 b. dx2 5 + 6y = 0 y(0) = – 1 (at x = 0) = 0 dx dx dy 2y = 0 0) = ? (McQuarrie 2-2)

Ive the following differential equations: а. dx2 - 4y = 0 y(0) = 2 (at x = 0) = 4 b. dx2 5 + 6y = 0 y(0) = – 1 (at x = 0) = 0 dx dx dy 2y = 0 0) = ? (McQuarrie 2-2)

Principles of Modern Chemistry
Principles of Modern Chemistry
8th Edition
ISBN:9781305079113
Author:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Publisher:David W. Oxtoby, H. Pat Gillis, Laurie J. Butler
Chapter4: Introduction To Quantum Mechanics
Section: Chapter Questions
Problem 9P: The maximum in the blackbody radiation intensity curve moves to shorter wavelength as temperature...
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Pls answer number 5 thank you
1. Before Planck's theoretical work on blackbody radiation, Wien showed empirically that AmaxT = 2.90 x10³ m-K where Amax is the wavelength at which the blackbody spectrum has its maximum value at a temperature T. This expression is called the Wien displacement law; derive it from the theoretical expression for the blackbody distribution. (McQuarrie 1-5) 2. Calculate the number of photons in a 2.00 mJ light pulse at (a) 1.06 µm, (b) 537 nm, and (c) 266 nm. (McQuarrie 1-13) 3. Given that the work function of chromium is 4.40 eV, calculate the kinetic energy of electrons emitted from a chromium surface that is irradiated with ultraviolet radiation of wavelength 200 nm. (McQuarrie 1-19) 4. A ground-state hydrogen atom absorbs a photon of light that has a wavelength of 97.2 nm. It then gives off a photon that has a wavelength of 486 nm. What is the final state of the hydrogen atom? (McQuarrie 1-26) 5. Calculate the de Broglie wavelength for (a) an electron with a kinetic energy of 100 eV, (b) a proton with a kinetic energy of 100 eV, and (c) an electron in the first Bohr orbit of a hydrogen atom. (McQuarrie 1-38) 6. If we locate an electron to within 20 pm, then what is the uncertainty in its speed? (McQuarrie 1-46)* 7. What is the uncertainty of the momentum of an electron if we know its position is somewhere in a 10 pm interval? How does the value compare to momentum of an electron in the first Bohr orbit? (McQuarrie 1-47)* 8. Solve the following differential equations: Y- 4y = 0 y(0) = 2 (at x = 0) = 4 а. dx2 d²y b. dx2 + 6y = 0 y(0) = – 1 (at x = 0) = 0 - 2y = 0 У(0) %3D 2 (McQuarrie 2-2) C. dx 9. Solve the following differential equations: + w?x(t) = 0 x(0) = 0 (at t = 0) = vo a. dt? d?x b. + w°x(t) = 0 x(0) = A (at t = 0) = vo Prove in both cases that x(t) oscillates with frequency w/2n. (McQuarrie 2-4) 10. Prove that the number of nodes for a vibrating string clamped at both ends is n - 1 for the nth harmonic. (McQuarrie 2-11)
Transcribed Image Text:1. Before Planck's theoretical work on blackbody radiation, Wien showed empirically that AmaxT = 2.90 x10³ m-K where Amax is the wavelength at which the blackbody spectrum has its maximum value at a temperature T. This expression is called the Wien displacement law; derive it from the theoretical expression for the blackbody distribution. (McQuarrie 1-5) 2. Calculate the number of photons in a 2.00 mJ light pulse at (a) 1.06 µm, (b) 537 nm, and (c) 266 nm. (McQuarrie 1-13) 3. Given that the work function of chromium is 4.40 eV, calculate the kinetic energy of electrons emitted from a chromium surface that is irradiated with ultraviolet radiation of wavelength 200 nm. (McQuarrie 1-19) 4. A ground-state hydrogen atom absorbs a photon of light that has a wavelength of 97.2 nm. It then gives off a photon that has a wavelength of 486 nm. What is the final state of the hydrogen atom? (McQuarrie 1-26) 5. Calculate the de Broglie wavelength for (a) an electron with a kinetic energy of 100 eV, (b) a proton with a kinetic energy of 100 eV, and (c) an electron in the first Bohr orbit of a hydrogen atom. (McQuarrie 1-38) 6. If we locate an electron to within 20 pm, then what is the uncertainty in its speed? (McQuarrie 1-46)* 7. What is the uncertainty of the momentum of an electron if we know its position is somewhere in a 10 pm interval? How does the value compare to momentum of an electron in the first Bohr orbit? (McQuarrie 1-47)* 8. Solve the following differential equations: Y- 4y = 0 y(0) = 2 (at x = 0) = 4 а. dx2 d²y b. dx2 + 6y = 0 y(0) = – 1 (at x = 0) = 0 - 2y = 0 У(0) %3D 2 (McQuarrie 2-2) C. dx 9. Solve the following differential equations: + w?x(t) = 0 x(0) = 0 (at t = 0) = vo a. dt? d?x b. + w°x(t) = 0 x(0) = A (at t = 0) = vo Prove in both cases that x(t) oscillates with frequency w/2n. (McQuarrie 2-4) 10. Prove that the number of nodes for a vibrating string clamped at both ends is n - 1 for the nth harmonic. (McQuarrie 2-11)
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