Calculating the wavelength of an electron

[bobsmith76]

Homework Statement

Calculate the wavelength of a beta particle (electron) that has an energy of 4.35 × 104 eV

Homework Equations

E = hf
λ = h/mv
V = W/q
eV = .5mv^2

The Attempt at a Solution

I can't figure out how to get electron volts into a form of energy that I'm familiar with in an equation. I tried

eV = .5mv^2 , but that gave me a speed above the speed of light.

I also tried using E = hf, but that also gave me a ridiculous number.

 

[PeterO]

Homework Statement

Calculate the wavelength of a beta particle (electron) that has an energy of 4.35 × 104 eV

Homework Equations

E = hf
λ = h/mv
V = W/q
eV = .5mv^2

The Attempt at a Solution

I can't figure out how to get electron volts into a form of energy that I'm familiar with in an equation. I tried

eV = .5mv^2 , but that gave me a speed above the speed of light.

I also tried using E = hf, but that also gave me a ridiculous number.

The conversion factor for swapping between eV and Joules is 1.6 x 10^-19.

You either divide or multiply depending which way you are changing.

You should know which figure is bigger: either a few joules = lots of eV or a few eV = lots of joules. You thus multiply or divide to get the size of answer you need.

Think: if you multiply by 1.6 x 10^-19 will that give a bigger number or a smaller number? Dividing will give the opposite. What size of answer do you want?

 

[ehild]

1 eV = elementary charge * 1 V=1.602 x 10-¹⁹ J.

Apply relativity theory. The given energy is the kinetic energy of the particle (the energy it gains when accelerated by 4.35 x 10 ⁴ V. Find the relativistic momentum, and you get the wavelength as λ=h/p.

ehild

 

[bobsmith76]

I can't get it. I'm pretty sure I have to divide 4.35 * 10^4 by 1.6 * 10^-19, but that gives me 2.7 *10^23. I then plug that into the equation

E/h = f

which gives me 56 orders of magnitude. I then divide 1.6 * 10^-19 by 4.35 * 10^4 and that also gives me the wrong answer. I have a feeling that my second step of using the

E/h = f equation is wrong.

 

[ehild]

I can't get it. I'm pretty sure I have to divide 4.35 * 10^4 by 1.6 * 10^-19, but that gives me 2.7 *10^23.

In what units? You have to get joules.

I then plug that into the equation

E/h = f

It is valid for photons. The electron is not photon.

What do you know about Relativity Theory?

ehild

 

[bobsmith76]

ok, I got the joules to be 7.53 * 10^-18, using this website

http://www.unitconversion.org/energy/joules-to-electron-volts-conversion.html

I don't know how they got that number and would like to know. In any case, I then plugged that number into

.5mv^2 and E = mc^2, using 9.11*10^-31 for the mass. After I got v, I plugged that into

lambda = h/mv

and I was off by an order of magnitude, so I still am doing something wrong.

 

[ehild]

ok, I got the joules to be 7.53 * 10^-18, using this website

http://www.unitconversion.org/energy/joules-to-electron-volts-conversion.html

It is wrong.
Think: 1 eV is equiavalent to 1.6 x10^-19 Joule.
What about 2 eV? 10 eV? 10000 eV? 43500 eV?

ehild

 

[PeterO]

I can't get it. I'm pretty sure I have to divide 4.35 * 10^4 by 1.6 * 10^-19, but that gives me 2.7 *10^23. I then plug that into the equation

If dividing didn't work, why didn't you try multiplying?


E/h = f

which gives me 56 orders of magnitude. I then divide 1.6 * 10^-19 by 4.35 * 10^4 and that also gives me the wrong answer. I have a feeling that my second step of using the

E/h = f equation is wrong.

See above