Calculate the wavelength of electrons traveling at 1.15x10^5

[Anna Davis]

Homework Statement

Calculate the wavelength of electrons traveling at 1.15x10^5 m/s

Homework Equations

λ = h/m*v

Given values:
h=6.626x10^-34 J*s
m=9.11x10^-31kg
v=1.15x10^5 m/s

The Attempt at a Solution

I converted J*s to SI units (kg⋅m2⋅s−2) and then substituted out all known values, to get:
λ = (6.626x10^-34 kg⋅m2⋅s−2)/(9.11x10^-31kg)(1.15x10^5 m/s)

After canceling out like units and doing the math, I get:
λ = 6.00x10^-9m

The text gives the solution as 6.33nm. I can't figure out how they got there (and why they converted to nm?).

Is this an error in the text or (more likely) in my logic/calcuations?

Any/all input is appreciated. Thanks!

 

[Doc Al]

The text gives the solution as 6.33nm. I can't figure out how they got there (and why they converted to nm?).

Your expression is correct, just redo the arithmetic. For wavelengths that small, nm is a typical unit.

 

[Anna Davis]

Ah, good to know about nm... And I'll do the math again (hopefully better!). Thanks :)

 

[James Pelezo]

If interested, and using the wavelength determined in the above problem, calculate the amount of energy in 1 gram of electrons moving at the same speed. (See if you can get ∆E = 1.9 x 10⁴Kj/mole e^-'s = 3.45 x 10⁷Kj/g e^-'s. Compare: A candle flame generating q ~ 40.7 Kj/g from burning paraffin wax to the energy content of a gram of electrons traveling at 1.15 x 10⁵m/s. => You might find it very surprising. You are definitely on the right track. Good job!