Calculating Electron Kinetic Energy, Velocity, Momentum, and Wavelength

[Grybas]

Homework Statement

Some electrons are accelerated through a P.d. of 500 V.
[e = 1.6x10^-19 C, mass of electron = 9.1x10^-31 Kg, h = 6.6x10^-34 Js.]


1. What is the kinetic energy of one of the electrons in eV?

2. What is the velocity of one of the electrons?

3. What is the momentum of one of the electrons?

4. What is the wavelength of the electron?

 

[fzero]

What have you tried so far?

 

[Grybas]

I'm struggling at these questions, i tried working out kinetic energy but i need velocity, but in the question it doesn't tell me anything about the speed the electrons are traveling at.

 

[fzero]

If the initial kinetic energy is zero, what is the kinetic energy of a single electron after it has been accelerated through the potential difference?

 

[Grybas]

ok, i got that its 500 eV, now the velocity bit, not sure what formula to apply.

 

[fzero]

How are the velocity and kinetic energy usually related?

 

[Grybas]

2. V = KE / (1/2 * M) V = (8x10^-17) / (9.1x10^-31 /2) V = 1.76x10^14
is that right?

 

[fzero]

If we start with

$$\text{KE} = \frac{1}{2} mv^2,$$

then

$$v= \sqrt{ \frac{2 \text{KE}}{m}}.$$

Also when you do a numerical calculation, make sure to state all of the units and convert them when needed. You can often check whether a formula is correct by checking that the result has the correct units.

 

[Grybas]

2. v= √(1.6x10^-16 / 9.1x10^-31) v=1.33x10^7
3. p=mv p= (9.1x10^-31)x(1.33x10^7) p=1.21x10^-23
4. λ=h/p λ= (6.6x10^-34)/(1.21x10^-23) λ=5.45x10^-11

look ok?

 

[fzero]

The numbers look ok, but you should figure out the proper units for each of them.

 

[Grybas]

1. 500 eV
2. v= √(1.6x10^-16 / 9.1x10^-31) v=1.33x10^7 m/s
3. p=mv p= (9.1x10^-31)x(1.33x10^7) p=1.21x10^-23 Kg-m/s
4. λ=h/p λ= (6.6x10^-34)/(1.21x10^-23) λ=5.45x10^-11 m

Thanks a lot for the help! :)