De Broglie wavelength of nitrogen molecules

[Kavorka]

Homework Statement

According to statistical mechanics, the average kinetic energy of a particle at temperature T is 3kT/2, where k is the Boltzmann constant. What is the average de Broglie wavelength of nitrogen molecules at room temperature?

Homework Equations

KE = 3kt/2 = p²/2m
λ = h / p

The Attempt at a Solution

So p = (2KEm)^1/2, and inserting KE = 3kt/2
p = (3kTm)^1/2

And thus λ = h/p = h / (3kTm)^1/2

The only problem I have is that it seems like the units don't work out.
Inserting the units only into h / (3kTm)^1/2 :

(kg m² /s²)/((m² kg/s² K)(K)(kg))^1/2 =
(kg m² /s²)/(m kg/s) =
m/s, not m

Am I simplifying the units wrong or is the equation wrong?

 

[TSny]

Your units for h are not quite correct.

 

[Kavorka]

Ah I see its kg m² / s. Thanks!

 

[Kavorka]

I'm having another problem. When I plug the values in where h = 1.602177x10^-11 kg m²/s, k = 1.3806488 x 10^-23 m² kg/s² K, T = 293.15 K, and m = 4.651734 x 10^-26 kg/molecule

I get 6.741 x 10¹¹ m when the answer in the book is 0.0276 nm. I'm obviously doing something very wrong.

EDIT: Oop wrong value for h, that explains why several of my answers to different questions were wrong hehe nevermind