# What is the energy of this electron

1. Mar 7, 2007

### tup

1. The problem statement, all variables and given/known data
An electron in the beam of a typical television picture tube is accelerated through a potential difference of 2.0*10^4 V before it strikes the face of the tube. What is the energy of this electron, in electron volts, and what is its speed when it strikes the screen?

2. Relevant equations
delta V = delta Ep/q
Ek=0.5mv^2

3. The attempt at a solution
well, I used the first equation to find its electric potential energy, which is (2.0*10^4)*(1.6*10^-19), and that gives me 3.2*10^-15J

then since it's asking in eV, and 1eV = 1.6*10^-19J, i do (3.2*10^-15)/(1.6*10^-19), which gives me 2*10^4eV (exact number as we started).

I don't see anything wrong with the procedure but the answer is 2*10^-4eV. what did i do wrong?

as for speed: (im using my 2*10^4eV as the energy)
Ek=0.5mv^2, and energy in J is 3.2*10^-15J
so 3.2*10^-15 = 0.5 (9.11*10^-31)v^2
that gives me 8.4*10^7m/s, which is exactly the same as the answer.

therefore i'm assuming the answer key for the energy in eV is wrong, what do you think?

2. Mar 7, 2007

### cepheid

Staff Emeritus
The definition of an electron volt is the energy gained by an elementary charge (e.g. the charge on proton or electron) when moved through a potential difference of one volt. This is why it is such a convenient unit of energy for particle physics. You know by definition that if an electron goes through potential difference of 2.0*10^4 volts, it now has an energy of 2.0*10^4 electron volts.

Conclusion 1: It wasn't necessary to multiply the voltage by the charge in coulombs to get the energy in joules first. You're measuring charge in units of "elementary charges" instead now.

3. Mar 7, 2007

### denverdoc

Electron volts is weird. By definition, its 20,000V. I think its a misprint in your answer key and converting this potential energy to kinetic strikes me as sound.

4. Mar 8, 2007

### cepheid

Staff Emeritus
Huh? This doesn't make any sense. Did you understand what I wrote?

5. Mar 8, 2007

### Gyroscope

Shouldn't you use relativistic kinetic energy?

6. Mar 8, 2007

### denverdoc

I didn't, it was a simultaneous post, i was saying the same thing--by the definition of eV, the answer was 20,000.

7. Mar 9, 2007

### tup

yea, i asked my teacher and the answer was printed wrong. thx guys.