• Support PF! Buy your school textbooks, materials and every day products via PF Here!

What is the radius of the orbit of an electron

  • Thread starter henrco
  • Start date
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.

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.
 

gneill

Mentor
20,486
2,612
Compare the velocity you found to the speed of light. Does it make sense? :wink:
 
47
2
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
20,486
2,612
Shove: While the eV is indeed an energy unit, 1 eV ≠ 1 J . Look up its definition.
 
47
2
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
20,486
2,612
Yup. Much better! :approve:
 
47
2
Thank you very much, that was really very helpful.
I've a much better understanding of what I was doing wrong now.
 

Want to reply to this thread?

"What is the radius of the orbit of an electron" You must log in or register to reply here.

Related Threads for: What is the radius of the orbit of an electron

Replies
13
Views
31K
Replies
1
Views
2K
Replies
5
Views
16K
Replies
6
Views
3K
Replies
2
Views
806
  • Posted
Replies
4
Views
962

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top