Wavelength for an electron

Smythe

I'm trying to work out the wavelength of an electron with a kinetic energy of 1keV

So I intend on using
de Broglie wavelength λ = h/p

and

Relativistic mass equation
E^2 = p^2 c^2 + (m0)^2 c^4

then inputting the rest mass energy of an electron (511 keV) into the formula above. Though do I need to convert this first to kg?

Also, I'd still be left with two unknowns in mass eqn i.e. E and p, so how do I obtain the value for E?

Or am I going about this the wrong way?

Thank you.

citrus burst

Smythe wrote: »

I'm trying to work out the wavelength of an electron with a kinetic energy of 1keV

So I intend on using
de Broglie wavelength λ = h/p

and

Relativistic mass equation
E^2 = p^2 c^2 + (m0)^2 c^4

then inputting the rest mass energy of an electron (511 keV) into the formula above. Though do I need to convert this first to kg?

Also, I'd still be left with two unknowns in mass eqn i.e. E and p, so how do I obtain the value for E?

Or am I going about this the wrong way?

Thank you.

You are going about this alright, but there is a much easier formula that you can use.

λ = h/(mv) . (1 - v^2/c^2)^1/2

This is basically the formula you would have worked out if you had have followed through with what you were doing, although it is tricky enough.

The only unknown you have now is v, which you get by using

E = (1/2) m v^2
=> v =(2E/m)^1/2

Also you are given the energy of the system E. Its 1 keV

Smythe

Thanks very much for that citrus burst.