Achieve HW (Weeks 2-4) :Question# 15

[keeganslomba3g]

You use an electron microscope in which the matter wave associated with the electron beam has a wavelength of 0.0403 nm. What is the kinetic energy of an electron in the beam, expressed in electron volts?

My work:

Lambda= 0403 nm = 4.03 m x10^-11
m = 9.109 x 10^31kg

v = (h/lambda)/ mass
v = (6.62608 x 10^-34/ 4.03 x 10^-11)/ 9.109 x 10^-31 = .18 x 10^8

Ek = 1/2 (mv)^2
Ek = 1/2 (9.109 x 10^-34 g) * (.18 x 10^8)^2
Ek= .82 x 10^-18

1 eV = 1.602 x 10 ^-19

So....

Ek= .82 x 10^-18 / 1.602 x 10 ^-19 = .512 x 10^1

My Answer is incorrect = .512 x 10^1 eV

What am I doing wrong?

[Gretchen_Fan_3C]

For that question, my book says the wavelength is 0.0287nm instead. But what I did was I used the KE=1/2mv^2 equation and rearranged lambda=h/p to v=h/lambda*m and then I substituted it into the equation for KE and from that I got the joules then from there converted it into eV. Hope this helps! I think it may be wrong because you put the wrong wavelength

[keeganslomba3g]

This doesn't make sense since v = (h/lambda)/ mass is the same as v = (h) /(lambda *mass), they are just arranged differently. Also, how is my wavelength wrong?

[Gretchen_Fan_3C]

I don't know, but that's what I did and I got the correct answer. I used the equations to put what information I did have in terms of v so I was able to solve for the answer. The wavelength is not what you wrote down. At least in my book it doesn't have the same wavelength you have.