Magnitude of the current flowing around the nucleus in the Bohr mode

[munkhuu94]

magnitude of the "current" flowing around the nucleus in the Bohr mode

Homework Statement

According to the Bohr model, a hydrogen atom in its lowest energy state has a nucleus consisting of a single proton, which is orbited by a single electron. The speed of the electron is 2.19×106 m/s and the radius of its orbit (the "Bohr radiuis") is 5.29×10−11 m. What is the magnitude of the "current" flowing around the nucleus in the Bohr model?

radius=5.29e-11
v=2.19e6

Homework Equations

equation used : I=nAvq ( i was surfing internet and found this equation, i couldn't find equation from the book)



2nd try: equation : I = e*w, where e is elementary charge and w is revs/s.


3rd try: J=I/A J is magnitude of current density.

The Attempt at a Solution

1st: I= 1*2pi(5.29e-11)^2(2.19e6)(-1.6e-19)
I= -6.16e-30 A seems very wrong.

2nd;
e = 1.6022E-19
w = v/(2pi*r)
I = 9.46518E-4 A ( i found this on yahoo answers, but it wasn't right, and i never seen that equation before.)

3rd: I don't know how to find the current if i use this equation. Please help.

 

[jedishrfu]

What is the definition of the ampere? It should have something to do with columbs per second.

Now as the electron orbits the hydrogen atom at the speed you gave it will orbit how many times in one second?

Does that help?

 

[munkhuu94]

Oh, so 2pi(5.29e-11)/2.19e6 = 1.518e-16 s for 1 rev. 1/1.518e-16 = 6.588e15 rev. and do i just multiply by the charge? I=q*w
-1.6e-19(6.588e15)= .00105 is that right? I'm not sure because i didn't see that equation in the book.
Thanks. And since it's magnitude it should be negative right?

 

[jedishrfu]

velocity * 1 second =distance traveled in 1 second

distance / (2 * pi * radius) ==> # of revs in 1 second

# of revs ==> # electrons passing by in 1 second

# electrons / 6.241×10E18 ==> # colombs in 1 second ==> amperes

in your example you're squaring the r value why?

 

[HalfLostAndSearching]

I would like to clarify that the concept of "current" flowing around the nucleus in the Bohr model is not a scientifically accurate description. In the Bohr model, the electron is considered to be in a stationary orbit around the nucleus, and it does not move in a continuous circular path like a current. The concept of current is used to describe the flow of charged particles in a circuit or conductor. In the case of the Bohr model, the electron is not considered to be flowing like a current, but rather it is in a stable orbit around the nucleus.

However, if we were to calculate the magnitude of the current using the given information, we can use the equation for current density (J=I/A) where I is the current and A is the cross-sectional area of the orbit. Since the orbit is assumed to be circular, we can use the formula for the area of a circle (A=πr^2) to get:

A = π(5.29e-11)^2 = 8.81e-21 m^2

Now, we can use the equation I = e*w, where e is the elementary charge and w is the angular velocity of the electron. The angular velocity can be calculated using the formula w = v/r, where v is the speed of the electron and r is the radius of the orbit. So, we get:

w = (2.19e6 m/s)/(5.29e-11 m) = 4.14e16 revs/s

Plugging this into the equation for current, we get:

I = (1.6022e-19 C)(4.14e16 revs/s) = 6.63e-3 A

So, the magnitude of the current flowing around the nucleus in the Bohr model is approximately 6.63 milliamps. However, as mentioned earlier, this is not a scientifically accurate description and the concept of current does not apply to the Bohr model.