(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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Question

(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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