Determining the electron’s de Broglie wavelength, momentum, kinetic energy and speed when k = 50nm-1

Question

A free electron has wave function

 

 Ψ(x, t) = sin(kx − ωt)

 

• Determine the electron’s de Broglie wavelength, momentum, kinetic energy and speed when k = 50nm^-1

 

Also, I know that the equations relating the speed v, momentum p, de Broglie wavelength λ, wave number k, kinetic energy
E, angular frequency ω and group velocity vg for a nonrelativistic particle of mass. 

 

Regards!

 

Answer 1

I will give you the equations, and you do the calculations.

 

λ = h/p 

 

Momentum:  p = [h/(2π)]k

 

You can look up h, and plug in k to get p.

 

λ = h / [h/(2π)]k = 2π/k

 

Wavelength:  λ = 2π/k

 

Plug in the value of k and get λ.

 

Kinetic energy:  E = p²/(2m)

 

You already found p above.  Now plug in p and the rest mass of an electron in appropriate units to get E.

 

Speed:  v = p/m