EBK INTRODUCTION TO HEALTH PHYSICS, FIF
EBK INTRODUCTION TO HEALTH PHYSICS, FIF
5th Edition
ISBN: 9780071835268
Author: Johnson
Publisher: VST
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Chapter 3, Problem 3.19P
To determine

The velocity of the ground state electrons in hydrogen and in helium.

Expert Solution & Answer
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Answer to Problem 3.19P

Hydrogen: v=2.2×106m/sec

Helium: v=4.49×106m/sec

Explanation of Solution

Formula used:

The equation which is used to find the radii of the electronic orbits is:

  r=n2h24π2me2Zk0

Calculation:

To find the velocity of the hydrogen electron:

  n=1h=6.625×1034Jsecmelectron=9.11×1031kgZ=1k0=9×109Nm2/C2e=4.8×1010sC=4.8×1010sC×((1C3× 109Sc))=1.6×1019C

  r=n2h24π2me2Zk0

  r=12×(6.625× 10 34Jsec)24π2(9.11×1031kg)×(1.62× 10 19C)2×1×9×109Nm2/C2

  r=5.17×1011m

The velocity is determined by:

  v=nh2πrm=1×6.625×1034Jsec2π×5.17×1011m×9.11×1031kg

  =2.2×106m/sec

For helium, the same method is used.

  n=1h=6.625×1034Jsecmelectron=207×9.11×1031kg=1.89×1028kgZ=1k0=9×109Nm2/C2e=4.8×1010sC=4.8×1010sC×((1C3× 109Sc))=1.6×1019C

  r=n2h24π2me2Zk0

  r=12×(6.625× 10 34Jsec)24π2(9.11×1031kg)×(1.62× 10 19C)2×2×9×109Nm2/C2

  =2.58×1011m

The velocity is determined by:

  v=nh2πrm=1×6.625×1034Jsec2π×2.58×1011m×9.11×1031kg

  =4.49×106m/sec

Conclusion:

The velocity of the hydrogen electron is v =2.2×106m/sec and the velocity of the helium electron is v =4.49×106m/sec

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