- #1

bbbl67

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## Homework Statement

What is the radius of the orbit of an electron traveling at 9.0 x 10^6 m/s around a zinc nucleus which contains 30 protons?

## Homework Equations

I don't know if this problem can be solved quantum mechanically, all I can think of doing is solving it classically, using Coulomb's Law and Centripetal force.

(1) Centripetal Force:

F = (m v^2)/r |

r | radius

F | centripetal force

v | rotation speed

m | mass

https://is.gd/CL6WBe

(2) Coulomb's Law:

F = (Q_1 Q_2)/(4 pi e_0 r^2) | U = (Q_1 Q_2)/(4 pi e_0 r) |

F | force

Q_1 | charge 1

Q_2 | charge 2

r | distance

U | potential energy

e_0 | electric constant (˜ 8.854×10^-12 F/m)

(in vacuum)

https://is.gd/P5JR1H

## The Attempt at a Solution

Then you use the balance of forces to find the radius.

F(1) = F(2)

(m v^2)/r = (Q_1 Q_2)/(4 pi e_0 r^2)

r = (Q_1 Q_2)/(4 pi e_0 m v^2) = ?

Q_1 = 1 e = 1.6021766×10^-19 C

Q_2 = 30 e = 4.8065299×10^-18 C

m = 1 m_e = 9.109384×10^-31 kg

v = 9.0E+6 m/s

r = ( 1.6021766×10^-19 C * 4.8065299×10^-18 C) / ( 4 pi e_0 (9.109384×10^-31 kg) (9.0E+6 m/s)^2)

= 9.380143×10^-11 meters

= 93.80143 picometers

https://is.gd/ttIdyJ