(a) Calculate: (i) the energy spacing AE between the ground state and the first excited state of the hydrogen atom; (ii) and the ratio AE/E1 between the spacing and the ground state energy. (b) Consider now a macroscopic system: a simple pendulum which consists of a 5 g mass attached to a 2 m long, massless and inextensible string. Calculate (i) the total energy E1 of the pendulum when the string makes an angle of 60° with the vertical: (ii) the frequency of the pendulum's small oscillations and the energy AE of one quantum; and (iii) the ratio AE/E1. (c) Examine the sizes of the ratio AE/E1 calculated in parts (a) and (b) and comment on the importance of the quantum effects for the hydrogen atom and the pendulum.
(a) Calculate: (i) the energy spacing AE between the ground state and the first excited state of the hydrogen atom; (ii) and the ratio AE/E1 between the spacing and the ground state energy. (b) Consider now a macroscopic system: a simple pendulum which consists of a 5 g mass attached to a 2 m long, massless and inextensible string. Calculate (i) the total energy E1 of the pendulum when the string makes an angle of 60° with the vertical: (ii) the frequency of the pendulum's small oscillations and the energy AE of one quantum; and (iii) the ratio AE/E1. (c) Examine the sizes of the ratio AE/E1 calculated in parts (a) and (b) and comment on the importance of the quantum effects for the hydrogen atom and the pendulum.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![(a) Calculate: (i) the energy spacing AE between the ground state and the first excited
state of the hydrogen atom; (ii) and the ratio AE/E between the spacing and the ground state
energy.
(b) Consider now a macroscopic system: a simple pendulum which consists of a 5 g mass
attached to a 2 m long, massless and inextensible string. Calculate (i) the total energy E1 of
the pendulum when the string makes an angle of 60° with the vertical; (ii) the frequeney of the
pendulum's small oscillations and the energy AE of one quantum; and (iii) the ratio AE/E1.
(c) Examine the sizes of the ratio AE/E1 calculated in parts (a) and (b) and comment on
the importance of the quantum effects for the hydrogen atom and the pendulum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4d53b892-cbd2-41af-b7cc-74bc87b846cd%2F3573d5ac-bed1-4a2f-a7c0-557502b4b8d0%2F50ts5o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Calculate: (i) the energy spacing AE between the ground state and the first excited
state of the hydrogen atom; (ii) and the ratio AE/E between the spacing and the ground state
energy.
(b) Consider now a macroscopic system: a simple pendulum which consists of a 5 g mass
attached to a 2 m long, massless and inextensible string. Calculate (i) the total energy E1 of
the pendulum when the string makes an angle of 60° with the vertical; (ii) the frequeney of the
pendulum's small oscillations and the energy AE of one quantum; and (iii) the ratio AE/E1.
(c) Examine the sizes of the ratio AE/E1 calculated in parts (a) and (b) and comment on
the importance of the quantum effects for the hydrogen atom and the pendulum.
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