What is the radius of the orbit of an electron

In summary, the conversation discusses finding the radius of a circular orbit of a 4.76 keV electron moving perpendicular to a magnetic field. The correct formula for calculating the velocity of the electron is provided and the conversation goes on to discuss the use of the eV unit and the definition of 1 eV. Eventually, the correct velocity is calculated and it is noted that the electron is moving at about 13% of the speed of light.
  • #1
henrco
47
2

Hi All,

Having difficultly figuring out where I've gone wrong with this problem. Any guidance gratefully received.

1. Homework Statement


A 4.76 keV electron (an electron that has a kinetic energy equal to 4.76 keV) moves in a circular orbit that is perpendicular to a magnetic field of 0.392 T.

i) Find the radius of the orbit.

Homework Equations



KE = 0.5 m v^2

r = mv / qB (where r = radius, m = mass of electron, q = charge of electron and B = magnetic field)

The Attempt at a Solution



Given the KE and the mass, find the velocity v. KE = 4.76 x 10^3 eV and m = 9.109x10^-31 kg

v = sqrt ( (2xKE / m))

v = sqrt ( (2x(4.76x10^3)/9.109 x 10^-31))

v= 1.02 x 10^17 m/s

Now having found the velocity v, find the radius r.

r = mv / qB

r = (9.109x10^-31)(1.02 x 10^17) / (1.602x10^-19)(0.392)

r = 1.48 x 10^6 m

However this answer is wrong and I don't know where I'm going wrong. Any help greatfully recieved.
 
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  • #2
Compare the velocity you found to the speed of light. Does it make sense? :wink:
 
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  • #3
Now that you mention it, it's a rather daft velocity.

1) I'm sure I'm using the right formula : KE = .5 (m) v ^2
2) The rearrangement to obtain v on the LHS looks correct: v = sqrt ( (2xKE / m))
3) And the calculation is correct : v = sqrt ( (2x(4.76x10^3)/9.109 x 10^-31))
4) So it leads me to think that I have the wrong value for the energy of the electron in the formula which is generating such a large velocity. So there is some transformation I need to do to 4.76x10^eV...

However after looking back at my books and notes, I can't figure this one out.

Could you please push me in the right direction. A good strong shove would be appreciated :-)
 
  • #4
Shove: While the eV is indeed an energy unit, 1 eV ≠ 1 J . Look up its definition.
 
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  • #5
Thank you for that shove.

I misunderstood eV. I see the definition is : 1eV = 1.602 x 10^-19 J.
I should be using Joules for KE.

v = sqrt ( (2x(4.76x10^3 * 1.602x10^-19 )/9.109 x 10^-31))

v = 4.09 x 10^7 m/s

which is still about 13% of the speed of light, so rather fast...

Is this correct now?
 
  • #6
Yup. Much better! :approve:
 
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  • #7
Thank you very much, that was really very helpful.
I've a much better understanding of what I was doing wrong now.
 

FAQ: What is the radius of the orbit of an electron

What is the radius of the orbit of an electron?

The radius of the orbit of an electron is a measure of the distance between the electron and the nucleus of an atom.

Does every electron have the same orbit radius?

No, the radius of an electron's orbit can vary depending on the energy level of the electron and the type of atom it is in.

How is the radius of the orbit of an electron determined?

The radius of an electron's orbit is determined by the quantum numbers associated with the electron, which describe its energy, angular momentum, and orientation in space.

Can the radius of an electron's orbit change?

Yes, the radius of an electron's orbit can change if the electron gains or loses energy, causing it to move to a different energy level and therefore a different orbit radius.

Why is the radius of an electron's orbit important?

The radius of an electron's orbit is important because it helps to determine the size and structure of an atom, which in turn affects its chemical and physical properties.

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