# What is the radius of the orbit of an electron

#### henrco

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.

2. 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)

3. 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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#### gneill

Mentor
Compare the velocity you found to the speed of light. Does it make sense?

#### henrco

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 :-)

#### gneill

Mentor
Shove: While the eV is indeed an energy unit, 1 eV ≠ 1 J . Look up its definition.

#### henrco

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?

#### gneill

Mentor
Yup. Much better!

#### henrco

Thank you very much, that was really very helpful.
I've a much better understanding of what I was doing wrong now.

"What is the radius of the orbit of an electron"

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