Flow of electrons (electricity/mechanics problem)

[benji]

So here's the problem:

In a television picture tube, elections are accelerated from rest through a potential difference of 12,000 volts and move toward the screen of the tube. When the electrons strike the screen, x-ray photons are emitted. Treat the elections nonrelativistically and determine:

a) the speed of an electron just before is strikes the screen

b) the number of electrons arriving at the screen per second if the flow of electrons in the tube is 0.01 coulomb per second

I've already figured part a by setting potential energy (equalling charge multiplied by potential difference) equal to kinetic energy. My answer is 6.49*10^7 m/s.

However, b is where I'm having trouble. I don't know how to go about it. Could someone please point me in the right direction?

 

[stunner5000pt]

Since each electron has a charge of its own, the total charge for n number of electrons is the n times the charge of the electron
that is $$Q = Ne$$

 

[thepatientmental]

In order to solve part b, we need to use the formula for electric current, which is defined as the rate of flow of charge. This can be written as I = Q/t, where I is the current in amperes, Q is the charge in coulombs, and t is the time in seconds.

Since we are given that the flow of electrons in the tube is 0.01 coulomb per second, we can plug this into the formula and solve for the current:

I = 0.01 C/s

Next, we need to find the charge on each electron. This can be calculated using the formula Q = ne, where n is the number of electrons and e is the charge of an electron (1.6*10^-19 C).

We know that the potential difference is 12,000 volts, which is equivalent to 12,000 joules per coulomb. So, we can set up an equation using the potential energy formula and solve for n:

12,000 J/C = (1/2)mv^2

n * 1.6*10^-19 C = (1/2) * m * (6.49*10^7 m/s)^2

Solving for n, we get n = 2.85*10^14 electrons.

Now, we can plug this value into the formula for current and solve for the number of electrons arriving at the screen per second:

I = 0.01 C/s = (2.85*10^14 electrons)/t

Solving for t, we get t = 2.85*10^16 seconds.

Therefore, the number of electrons arriving at the screen per second is approximately 2.85*10^14 electrons.