Calculate wavelength of electron

[okgo]

Homework Statement

http://www.screencast.com/users/trinhn812/folders/Jing/media/9582a1aa-b21a-4e50-8774-b60866a7d666

Homework Equations

lambda=h/p

The Attempt at a Solution

So I got 4.04E-12 m but the book says the answer is 3.23pm

I'm not sure where I'm wrong

 

[rock.freak667]

The speed of the electron is 0.6c, so you need to to use

λ=h/γp where γ = 1/√(1-(v/c)²)

 

[okgo]

Thanks. So in addition to time dilation and length contraction, is this what you call momentum dilation?

 

[rock.freak667]

Thanks. So in addition to time dilation and length contraction, is this what you call momentum dilation?

Not sure if that is what it is called, but I call it momentum accounting for relativistic effects.

 

[rwisz]

.

First, let's define the variables:
- lambda is the wavelength of the electron
- h is Planck's constant (6.626 x 10^-34 m^2 kg/s)
- p is the momentum of the electron

To calculate the wavelength of the electron, we need to know the momentum. From the image provided, we can see that the momentum is 3.25 x 10^-24 kg m/s.

Now, let's plug in the values into the equation:
lambda = (6.626 x 10^-34 m^2 kg/s) / (3.25 x 10^-24 kg m/s)
= 2.04 x 10^-10 m

This result is in meters, but the book answer is in picometers (pm). To convert meters to picometers, we need to multiply by 10^12.
Therefore, the final answer is 2.04 x 10^-10 m x 10^12 = 2.04 x 10^2 pm = 204 pm.

So, the book answer of 3.23 pm is incorrect. The correct answer is 204 pm.