   Chapter 31, Problem 10PE

Chapter
Section
Textbook Problem

The unified atomic mass unit is defined to be 1   u = 1.6605 × 10 − 27 kg . Verify that this amount of mass converted to energy yields 931.5 MeV. Note that you must use four—digit or better values for c and | q e | .

To determine

If a mass of 1 u when converted into energy, yields 931.5 MeV.

Explanation

Given info:

The value of 1 unified atomic mass unit in kg

m=1.6605×1027kg

Speed of light (from std tables)

c=2.99792×108m/s

Charge of an electron (from std tables)

qe=1.602177×1019C

Formula used:

If a mass m is converted into energy, then the energy is given by,

E=mc2

Calculation:

Calculate the energy released when 1 u mass is converted into energy.

E=mc2=1.6605×1027kg2.99792× 108m/s2=1.49238×1010J

One electron volt is the energy gained by an electron when accelerated through a potential of 1 V. Therefore,

E=qe1 V=1 eV=1

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