Modern Physics for Scientists and Engineers
Modern Physics for Scientists and Engineers
4th Edition
ISBN: 9781133103721
Author: Stephen T. Thornton, Andrew Rex
Publisher: Cengage Learning
Question
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Chapter 4, Problem 21P
To determine

Use the known values of ε0,h,mande to calculate the following to five significant figures:

hc(ineVnm),e2/4πε0(ineVnm),mc2(inKeV),a0(innm)andE0(ineV) .

Expert Solution & Answer
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Answer to Problem 21P

Using the known values of ε0,h,mande values of the following expressions hcis1239.8eVnm_, e2/4πε0 is 1.4400eVnm_ , mc2 is 511.00KeV_, a0is5.2918×102nm_, and E0 is 13.606eV_

s calculated below.

Explanation of Solution

Calculate hc:

Here, h is the Plank’s constant and c is the speed of photon.

Substitute 4.135669×1015eVs for h and 299792458m/s for c in above expression.

hc=(4.135669×1015eVs)(299792458m/s)=1.2398×106eVm=1239.8eVnm

Calculate e2/4πε0:

Here, e is the charge in electron.

Substitute 1.6021733×1019C for e and 8.8541878×1012F/m for ε0 in above expression.

e2/4πε0=(1.6021733×1019C)24π(8.8541878×1012F/m)(1eV1.6021733×1019Nm)(109nm1m)=1.4400eVnm

Calculate mc2:

Here, m is the mass of electron.

Substitute 9.10938356×1031kg for m and 299792458m/s for c in above expression.    mc2=(9.10938356×1031kg)(299792458m/s)21.602176×1019CeV=510999 eV=511.00KeV

Calculate a0:

Write the expression for a0.

    a0=4πε0h2me2

Here, a0 is the Bohr’s radius,  and (h) is the h - bar constant .

Substitute 9.10938356×1031kg for m, 1.055×1034kgm/s2 for (h), 1.6021733×1019C for e and 8.8541878×1012F/m for ε0 in above expression.   

a0=4π(8.8541878×1012F/m)(1.055×1034kgm/s2)2(9.10938356×1031kg)(1.6021733×1019C)2=5.2918×1011m=5.2918×102nm

Calculate E0:

Write the expression for E0.

    E0=e28πε0a0

Here, E0 is the Energy.

Substitute 5.2918×1011m for a0, 1.6021733×1019C for e and 8.8541878×1012F/m for ε0 in above expression.   

E0=(1.6021733×1019C)28π(8.8541878×1012F/m)(5.2918×1011m)=2.179874×1018J(1eV(1.6021733×1019J))=13.606eV

Conclusion:

Thus, using the known values of ε0,h,mande values of the following expressions hcis1239.8eVnm_, e2/4πε0 is 1.4400eVnm_ , mc2 is 511.00KeV_, a0is5.2918×102nm_, and E0 is 13.606eV_

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