   Chapter 31, Problem 75PE

Chapter
Section
Textbook Problem

The purpose of this problem is to show in three ways that the binding energy at the election in a hydrogen atom is negligible compared with the masses of the proton and electron. (a) Calculate the mass equivalent in u of the 13.6−eV binding energy of an electron in a hydrogen atom, and compete this with the mass of the hydrogen atom obtained from Appendix A. (b) Subtract the mass at the proton given in Table 31.2 from the mass at the hydrogen atom given in Appendix A. You will find the difference is equal to the electron’s mass to three digits, implying the binding energy is small in comparison. (c) Take the ratio of the binding energy at the electron (13.6 eV) to the energy equivalent of the electron's mass (0.511 MeV). (d) Discuss how your answers confirm the stated purpose of this problem. (a)

To determine

The mass equivalent in u and compare this with the mass of hydrogen atom.

Explanation

Given info:

The binding energy of an electron in hydrogen atom is

E=13.6eV

Formula used:

The energy mass relation is

E=mc2

m=Ec2

Calculation:

Substituting the values

m=13.6eV/c2931.5MeV/c2

m=13.6eV931

(b)

To determine

The difference between proton mass to the hydrogen mass.

(c)

To determine

Ratio of binding energy of 13.6eV to the binding energy of electron.

(d)

To determine

The stated purpose of this problem.

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