Speed with a de Broglie wavelength.

[elephantorz]

1. At what speed is an electron's de Broglie wavelength:
(a) 1.0 pm
(b) 1.0 nm
(c) 1.0 \mum
(d) 1.0 mm2. \lambda = \frac{h}{mv}
3. I have solved for v, and I plugged in values, it gives me, for a = 4.54 x 10^(27) m/s, the ANSWER is: 2.77 x 10^(8) ms, it's way off, I tried converting energy into Js it also did not work, what am I overlooking?

 

[elephantorz]

Is it possible that my teacher is wrong? I think she copied down her answer wrong on my paper...

 

[Nick89]

I am not sure on this one, should you perhaps take into account the relativistic speed?
\lambda = \frac{h}{m \gamma v}

For a I get:
v = \frac{h}{m \lambda} = \frac{6.63 \times 10^{-34}}{(9.109 \times 10^{-31})(1\times 10^{-12})} = 7.28 \times 10^8 \text{m/s}
This is higher than the speed of light and can therefore never be correct.


Your answer of 4.54 x 10^27 m/s is ridiculously high. The answer can NEVER be more than the speed of light which is approximately 3.0 x 10^8 m/s.


EDIT
Using 2.77 x 10^8 as the speed, you get a wavelength of 2.63 x 10^-12 m or 2.63 ps. Something wrong with the question maybe?

 

[alphysicist]

The formula with the relativistic momentum in Nick89's post will give the correct answer.