Electron velocity of 2.5 x 10^6 ms^-1 and has a mass of 9.109 x 10^-2g, what is it's wave length?

Question

Wavelength = Placnk's constant/mv

Lambda = h/mv

h = 6.626 x 10^-34 Js

m = 9.109 x 10^-28 g

v = 2.5 x 10^6 ms^-1

6.626 x 10^-34 Js

--------------------------

9.109 x 10^-28g x 2.5 x 10^6 ms^-1

It comes out to be 2.9 x 10^-13 Js/gms^-1.

is this a wave length? wtf? Or am i doing something wrong?

Answer 1

You're right-ish.  You've just skipped over some conversion steps that will give you a more familiar answer.  First, always convert grams to kilograms.  Once you've plugged in your given values and solved, you want to use the conversion factor for Joules (1 kg * m^2/s^2 = 1 J).  And finally, you want to convert meters to nanometers.

First convert grams to kilograms:

[1] 9.109 * 10^-28 grams = 9.109 * 10^-31 kilograms.

Plug your values in for h, m and v:

[2A] Wavelength = (6.626*10^-34 J-s) / (9.109*10^-31 g)*(2.5*10^6 m/s)

[2B] Wavelength = 2.910*10^-10 J-s^2/g-m

Convert Joules:

[3A] (2.910*10^-10 J-s^2/kg-m) * [(1 kg * m^2/s^2) / (1 J)]

[3B] = 2.910*10^-10 m.

You're nearly finished, but since wavelength is normally reported in nanometers, we convert again:

[4] (2.910*10^-10 m) * (1 nm / 10^-9 m) = .2910 nm.

You're done.