Speed of Electron in Orbit

In summary, an electron needs to orbit the sphere 1.50mm above the surface at a speed of 4.69*10^7 m/s in order to maintain an electric force of 8.99*10^9 N.
  • #1
tomizzo
114
2

Homework Statement



A 2.70-mm-diameter glass sphere has a charge of + 1.10 nC.

What speed does an electron need to orbit the sphere 1.50mm above the surface?

Homework Equations



a = v^2/r -> force = m*v^2/r

electrostatic force = K*Q1*Q2/distance^2

therefore:

m*v^2/r=K*Q1*Q2/distance^2

The Attempt at a Solution



(9.10938291 × 10-31 kg)(v^2)/((2.7*10^-3)/2) = 8.99*10^9*(1.60*10^-19)*(1.1*10^-9)/(1.50*10^3)^2

I get 32282518 m/s which is the incorrect answer. However, I just noticed something. The radius I'm using is half of the sphere, should I be adding the separation distance to the radius as well?
 
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  • #2
yes, the circle's radius is bigger than the glass radius.
 
  • #3
lightgrav said:
yes, the circle's radius is bigger than the glass radius.

I got an answer of 4.69*10^7 m/s and it still says it's incorrect.
 
  • #4
I didn't get that speed. why don't you cancel one of the radius variables, and try the calculation again.
 
  • #5
Here are my values:

Mass of electron = 9.10938*10^-31 kg
v = ?
radius = half of glass sphere plus separation distance = (2.7/2)*10^-3+1.5*10^-3
K = 8.99*10^9
Q1 = 1.6*10^-19 (charge of electron in coulombs)
Q2 = 1.1*10^-9
distance = 1.5*10^-3

Now I'm realizing the distance should probably be (2.7/2)*10^-3+1.5*10^-3 also...
 
  • #6
With the change, I'm getting an answer of 2.469*10^7 m/s. Does this look familiar?
 
  • #7
I think it rounds up to 24.7 Mm/s ... the E-field has spread more at that distance, so is weaker at the electron.
 
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  • #8
Well, this is obviously way too late, but for all of you physics nerds out there here it is.

Uniformly Charged Sphere Equation:

E=Q/(e0*4*r^2*pi)

E=electric field
Q=charge of sphere 1.1*10^-9 (in this case)
e0=8.85*10^-12
r=1.5*10^-3 (in this case)
pi = pi ;)

Take that E and plug it into the following Electric Force Equation:

E=F/q

E= what you solved for previously
F=Force that you want to derive
q=1.6*10^-19 (constant for charge of electron)

Take that F and plug it into this standard Force Equation:

F=ma

F=what you solved for previously
m=9.11*10^-31
a=what you want to solve forLast, but not least plug the a you solved for into the following Uniform Circular Motion Equation:

a=v^2/r

a=what you just solved for
v=what you want to solve for
r=1.5*10^-3 (in this case)That's it ladies and gents. Physics = MAGIC
 

1. What is the speed of an electron in orbit?

The speed of an electron in orbit is dependent on its energy level and the distance from the nucleus. In general, the speed can range from 0.5% to 2.5% of the speed of light, which is approximately 1,000 to 5,000 kilometers per second.

2. How does the speed of an electron change in different energy levels?

As an electron moves to a higher energy level, its speed increases. This is because the electron is further from the nucleus and experiences less attraction, allowing it to move faster. Conversely, when an electron moves to a lower energy level, its speed decreases.

3. Can the speed of an electron in orbit be measured?

Yes, the speed of an electron in orbit can be measured using a variety of methods, such as spectroscopy or electron microscopy. However, due to the uncertainty principle in quantum mechanics, the exact speed and position of an electron cannot be simultaneously determined.

4. How does the speed of an electron in orbit contribute to an atom's properties?

The speed of an electron in orbit is one of the factors that determines an atom's properties, such as its size, reactivity, and chemical bonding behavior. The speed also affects an atom's emission and absorption spectra, which are used to identify elements.

5. Is the speed of an electron in orbit constant?

No, the speed of an electron in orbit can vary depending on its energy level and the external factors affecting it, such as temperature and electric fields. In addition, the speed of an electron in a circular orbit is not constant as it is constantly changing direction and velocity due to the uncertainty principle.

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