Radius and period of charge in B field

[velocity9]

Homework Statement

A doubly charged helium atom (mass = 6.68 x 10-27 kg) is accelerated through a potential difference of 4.00x 103 V. What will be the radius of curvature of the path of the atom if it is in a uniform 0.460 T magnetic field?
Note: I hope this question is meant in advanced physics >.<
If not, I apologize. Please direct me towards the proper place.

Homework Equations

r = (mv)/(qB)

E = qV

K = ½mv^2

The Attempt at a Solution

I let
E=K and so
½mv^2 = qV
I solved for v which gave me
v = √((2*q*V)/m)
I subbed this v into
r = (mv)/(qB)

I know from the information provided that
B = 0.460 T
m = 6.68*10^-27 kg
V = 4.00*10^3
and I know q = 2*e
I also found v so there aren't any other unknowns, I subbed in...
I got 0.0199 m for r but my answer is said to be wrong. Not sure where I made a mistake. Any help is appreciated! Thank you

 

[TSny]

Welcome to PF!

Your work looks correct. Maybe you made a mistake in plugging in the numbers. What did you get for the speed v?

 

[velocity9]

Welcome to PF!

Your work looks correct. Maybe you made a mistake in plugging in the numbers. What did you get for the speed v?

I got 437740 m/s for the speed

 

[TSny]

I think you might not have used the correct charge. Note that 2q = 4e.

 

[velocity9]

I think you might not have used the correct charge. Note that 2q = 4e.

gaah yes you are right! So sorry for the silly mistake. I had it written down correctly but my brain wouldn't convey the information to my fingers when plugging into the calculator. Thank you so much for your time!

 

[TSny]

OK. Nice work!

 

[velocity9]

OK. Nice work!

For the second part of the question, it asks:
What is the period of revolution for the atom in the previous question?

I'm having a little bit of trouble deciding what is related to what. I figure I can use

ω = 2π/T

the velocity found.. that is ω, right?
Not sure how else they could be connected. I tried thinking in terms of centripetal velocity but that didn't get me anywhere.
Thank you in advance!

 

[gneill]

What's the length of the path that the atom follows? What's its speed around that path? How long does it take to cover that distance at that speed?

 

[velocity9]

What's the length of the path that the atom follows? What's its speed around that path? How long does it take to cover that distance at that speed?

I know the velocity since I found it in the first part. I used

v = √((2*q*V)/m)

and found v = 6.19*10^5 m/s
I think the time to cover that distance would be the period. If I could find the distance, I could probably use simple v = d/t and rearranging for t=d/v, I think the units cancel to leave you with seconds which is the unit of period. I think.
The distance I'm kind of confused about. It's not simply the radius. I would look for a circumference or something of the sort but I'm not even sure the exact shape of the path. Do I need to know if it's a circle or something like that or am I going in the wrong direction again haha
Thank you for your time!

 

[gneill]

Well, you found a radius. What did you equate in order to find it? (What's it the radius of?)

 

[velocity9]

Well, you found a radius. What did you equate in order to find it? (What's it the radius of?)

Ok, so I found that mutiplying the d/v that we were discussing by 2pi works. I realize the units are convenient as we had discussed since all we are left with is seconds. I'm not entirely sure why the 2pi worked. I was searching about period and I noticed most of the periods had 2pi written next to them so I figured I would try but is it simply a matter of period having to be related with pi? Just trying to understand how my lucky guess worked. Thanks!

 

[gneill]

What is the relationship between the radius and circumference of a circle?

 

[velocity9]

What is the relationship between the radius and circumference of a circle?

Thank you so much for your patience! It all makes sense now