Electrons in a TV tube accelerated from rest.

[_F_]

Homework Statement

Electrons in a TV tube are accelerated from rest through a 25-kV potential difference. With what speed do they hit the TV?

V = 25*10^3 J/C

Homework Equations

I'm not really sure here. I'm thinking you have to use Newtonian mechanics somewhere here.
So,
x(t) = (1/2)(a_x)t^2 + (v_0)t +x_0
(v_f)^2 = (v_0)^2 + 2(a_x)d

You also need electomagnetic equations.
So,
delta-V = delta-U/q = -E*delta-r

The Attempt at a Solution

This is where I have trouble. I don't even know where to start. Any pointers in the right direction (that aren't too vague!) would greatly be appreciated.

 

[tiny-tim]

Welcome to PF!

Electrons in a TV tube are accelerated from rest through a 25-kV potential difference. With what speed do they hit the TV?

V = 25*10^3 J/C

Hi _F_! Welcome to PF!

Hint: volts = energy/charge (as you can see from the J/C units).

So what KE does each electron have after going through a 25kV potential difference?

 

[_F_]

Hi _F_! Welcome to PF!

Hint: volts = energy/charge (as you can see from the J/C units).

So what KE does each electron have after going through a 25kV potential difference?

Okay, so K = (1/2)mv^2

We have volts in J/C, so to get a value of just energy would we multiply V*q?
If so:
V*q = (2.5*10^3 J/C)(1.6*10^-19 C) = 4*10^-16 J.

So K = 4*10^-16 J,
Then
K/[(1/2)m] = v^2 => (4*10^-16 J)/[(1/2)(9.1*10^-31 kg) = 8.79*10^14 J/kg

So v^2 = 8.79*10^14 J/kg
Then, v = sqrt(8.79*10^14 J/kg) = 2.9*10^7 m/s

But this is not what the back of my book says. In the back, the answer is 9.37*10^7 m/s.

 

[tiny-tim]

Okay, so K = (1/2)mv^2

We have volts in J/C, so to get a value of just energy would we multiply V*q?
If so:
V*q = (2.5*10^3 J/C)(1.6*10^-19 C) = 4*10^-16 J.

So K = 4*10^-16 J,
Then
K/[(1/2)m] = v^2 => (4*10^-16 J)/[(1/2)(9.1*10^-31 kg) = 8.79*10^14 J/kg

So v^2 = 8.79*10^14 J/kg
Then, v = sqrt(8.79*10^14 J/kg) = 2.9*10^7 m/s

But this is not what the back of my book says. In the back, the answer is 9.37*10^7 m/s.

Hi _F_!

Hint: check your units … you're out by a factor of √10.

 

[_F_]

Hi _F_!

Hint: check your units … you're out by a factor of √10.

J = kg*m^2/s^2

V = [J/C]
Vq = [J]
K = [J]
v^2 = 2K/m = [m^2/s^2]
v = [m/s]

Where did I go wrong?

 

[Dick]

J = kg*m^2/s^2

V = [J/C]
Vq = [J]
K = [J]
v^2 = 2K/m = [m^2/s^2]
v = [m/s]

Where did I go wrong?

V is given to be 25*10^3 J/C. You used 2.5*10^3.

 

[_F_]

V is given to be 25*10^3 J/C. You used 2.5*10^3.

Ack! Thanks. Such a stupid mistake.