Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 29, Problem 5P
(a)
To determine
The
(b)
To determine
The corresponding quantum number of the moon’s angular momentum.
(c)
To determine
The fraction of Earth-moon distance increased to raise quantum number by 1.
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Calculate the angular momentum of the Moon due to its orbital motion about Earth. In your calculation use 3.84 x 108 m as the average Earth–Moon distance and 2.36 x 106 s as the period of the Moon in its orbit. (b) If the angular momentum of the Moon obeys Bohr’s quantization rule (L = n h), determine the value of the quantum number n. (c) By what fraction would the Earth–Moon radius have to be increased to increase the quantum number by 1?
A) By what factor is the uncertainty of the electron's position(1.36×10-4 m) larger than the diameter of the hydrogen atom?(Assume the diameter of the hydrogen atom is 1.00×10-8 cm.)
B) Use the Heisenberg uncertainty principle to calculate Δx for a ball (mass = 122 g, diameter = 8.50 cm) with Δv = 0.425 m/s.
C) The uncertainty of the (above) ball's position is equal to what factor times the diameter of the ball?
An atom of iron has a radius of
156. pm
and the average orbital speed of the electrons in it is about
×5.7*10^7 m/s.
Calculate the least possible uncertainty in a measurement of the speed of an electron in an atom of iron. Write your answer as a percentage of the average speed, and round it to 2 significant digits.
Chapter 29 Solutions
Principles of Physics: A Calculus-Based Text
Ch. 29.2 - Prob. 29.1QQCh. 29.2 - Prob. 29.2QQCh. 29.4 - Prob. 29.3QQCh. 29.5 - Prob. 29.4QQCh. 29.6 - Prob. 29.5QQCh. 29.6 - Prob. 29.6QQCh. 29 - Prob. 1OQCh. 29 - Prob. 2OQCh. 29 - Prob. 3OQCh. 29 - Prob. 4OQ
Ch. 29 - Prob. 5OQCh. 29 - Prob. 6OQCh. 29 - Prob. 7OQCh. 29 - Prob. 8OQCh. 29 - Prob. 9OQCh. 29 - Prob. 10OQCh. 29 - Prob. 1CQCh. 29 - Prob. 2CQCh. 29 - Prob. 3CQCh. 29 - Prob. 4CQCh. 29 - Prob. 5CQCh. 29 - Prob. 6CQCh. 29 - Prob. 7CQCh. 29 - Prob. 8CQCh. 29 - Prob. 9CQCh. 29 - Prob. 10CQCh. 29 - Prob. 1PCh. 29 - Prob. 2PCh. 29 - Prob. 3PCh. 29 - Prob. 4PCh. 29 - Prob. 5PCh. 29 - Prob. 6PCh. 29 - Prob. 7PCh. 29 - Prob. 8PCh. 29 - Prob. 10PCh. 29 - Prob. 11PCh. 29 - Prob. 12PCh. 29 - Prob. 13PCh. 29 - Prob. 14PCh. 29 - Prob. 15PCh. 29 - Prob. 16PCh. 29 - Prob. 17PCh. 29 - Prob. 18PCh. 29 - Prob. 19PCh. 29 - Prob. 20PCh. 29 - Prob. 21PCh. 29 - Prob. 22PCh. 29 - Prob. 23PCh. 29 - Prob. 24PCh. 29 - Prob. 25PCh. 29 - Prob. 26PCh. 29 - Prob. 27PCh. 29 - Prob. 28PCh. 29 - Prob. 29PCh. 29 - Prob. 30PCh. 29 - Prob. 31PCh. 29 - Prob. 32PCh. 29 - Prob. 33PCh. 29 - Prob. 34PCh. 29 - Prob. 35PCh. 29 - Prob. 36PCh. 29 - Prob. 37PCh. 29 - Prob. 38PCh. 29 - Prob. 39PCh. 29 - Prob. 40PCh. 29 - Prob. 41PCh. 29 - Prob. 42PCh. 29 - Prob. 43PCh. 29 - Prob. 44PCh. 29 - Prob. 45PCh. 29 - Prob. 46PCh. 29 - Prob. 47PCh. 29 - Prob. 48PCh. 29 - Prob. 49PCh. 29 - Prob. 50PCh. 29 - Prob. 51PCh. 29 - Prob. 52PCh. 29 - Prob. 53PCh. 29 - Prob. 54PCh. 29 - Prob. 55PCh. 29 - Prob. 57PCh. 29 - Prob. 58PCh. 29 - Prob. 59PCh. 29 - Prob. 60PCh. 29 - Prob. 61PCh. 29 - Prob. 63PCh. 29 - Prob. 64PCh. 29 - Prob. 65PCh. 29 - Prob. 66P
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- (a) Calculate the angular momentum of the Moon due to its orbital motion about Earth. In your calculation use 3.84 x 10⁰ m as the average Earth- Moon distance and 2.36 × 106 s as the period of the Moon in its orbit. (Use 7.36 × 1022 kg for the mass of the moon.) 2.889e34 kg. m²/s (b) If the angular momentum of the moon obeys Bohr's quantization rule (L = nħ) determine the value of the quantum number, n. 8.463e67 Your response differs from the correct answer by more than 10%. Double check your calculations. (c) By what fraction would the Earth-Moon radius have to be increased to increase the quantum number by 1? 2.3632e-6 X Your response differs from the correct answer by more than 100%.arrow_forward(a) Calculate the angular momentum of the Moon due to its orbital motion about Earth. In your calculation use 3.84 × 108 m as the average Earth- Moon distance and 2.36 × 106 s as the period of the Moon in its orbit. (Use 7.36 × 1022 kg for the mass of the moon.) kg. m²/s 2.889e34 (b) If the angular momentum of the moon obeys Bohr's quantization rule (L: nh) determine the value of the quantum number, n. 2.7395e68 (c) By what fraction would the Earth-Moon radius have to be increased to increase the quantum number by 1? 1.825e-69 X Your response differs from the correct answer by more than 10%. Double check your calculations.arrow_forward(a) Calculate the angular momentum of the Moon due to its orbital motion about Earth. In your calculation use 3.84 × 108 m as the average Earth−Moon distance and 2.36 × 106 s as the period of the Moon in its orbit. (b) If the angular momentum of the Moon obeys Bohr’s quantization rule (L=nh), ), determine the value of the quantum number n. (c) By what fraction would the Earth−Moon radius have to be increased to increase the quantum number by 1?arrow_forward
- Write an expression relating the kinetic energy KE of the electron and the potential energy PE in the Bohr model of the hydrogen atom. (a) Suppose a hydrogen atom absorbs a photon of energy E, resulting in the transfer of the electron to a higher - energy level. Express the resulting change in the potential energy of the system in terms of E. (b) What is the change in the electron’s kinetic energy during this process?arrow_forwardIt may be argued on theoretical grounds that the radius of the hydrogen atom should depend only on the fundamental constants h, e, the electrostatic force constant k = 1/4πℰ0, and m (the electron’s mass). Use dimensional analysis to show that the combination of these factors that yields a result with dimensions of length is h2kme2.arrow_forwardUsing the Boh model of an electron orbiting a nucleus, the angular momentum of Earth's orbit around the Sun is 2.67 x 1040 g m2 s−1. Using the Bohr quantization condition, what is the quantum number n for Earth's orbit? If the Earth transitions from this orbit to n-1 (emitting a graviton, which is the gravitational anagloue of the photon), how much energy would be released? Find the frequency of the graviton.arrow_forward
- Prove that, to three-digit accuracy, h = 4.14×10−15 eV ⋅ s, as stated in the text.arrow_forwardWhat is the average radius of the orbit of an electron in the n=2 energy level of an oxygen atom (Z=8)? Express your answer in pico-meters.arrow_forwardThe energy levels of the Bohr model for the atom can be expressed mathematically as En -13.6 eV, where Z is the atomic number, and n is the quantum number. This model is reasonably accurate for hydrogen and for singly ionized helium. The photon associated with the transition of an electron from the ground state to the first excited state in singly ionized helium has a different wavelength than that associated with a similar transition in hydrogen. Which of the following correctly describes the wavelengths of these two photons in terms of the energy level diagrams for hydrogen and helium? The photon absorbed by hydrogen has a longer wavelength than that absorbed by helium, because the energy levels in the diagram for hydrogen are more closely spaced than in the diagram for helium. B The photon absorbed by hydrogen has a shorter wavelength than that absorbed by helium, because the energy levels in the diagram for hydrogen are more closely spaced than in the diagram for helium. The photon…arrow_forward
- A hypothetical molecule oscillates with a natural frequency of 1.4 × 1013 Hz. Part (a) What is the energy difference, in electron volts, between adjacent harmonic oscillator states of the hypothetical molecule? Part (b) What is the quantum number of the state of the hypothetical molecule that has an energy of 0.75 eV? Round your answer to the nearest integer.arrow_forwardA certain atom remains in an excited state for about 51.7 ns before emitting a 2.15-eV photon and transitioning to the ground state. What is the uncertainty in the frequency of the photon in Hz?arrow_forwardIn this problem, you will calculate the center of mass of two molecules. For each molecule, draw a picture. Clearly indicate the origin of your coordinate system, the locations of the atoms, and the location of the center of mass. Consult a periodic table to find the masses of the atoms. (a) Electron diffraction experiments reveal that the distance between the centers of the carbon (C) and oxygen (O) atoms in a carbon monoxide molecule is about 1.100 x 10-10 m. Where is the center of mass of a CO molecule? (b) In an ammonia molecule (NH3), the atoms are arranged in a pyramid.* The three hydrogen atoms (H) form an equilateral triangle at the base of a pyramid. The distance between the centers of the hydrogen atoms is 1.628 x 10-10 m; thus, the center of the triangle is 9.399 x 10-"m from each hydrogen atom. The nitrogen atom (N) sits at the apex of the pyramid. The distance between the center of the nitrogen atom and any hydrogen atom is 1.014 x 10-10 m. Where is the center of mass of…arrow_forward
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