Question

Using Planck’s constant as h = 6.63 E-34 J*s, what is the wavelength of a proton with a speed of 5.00 E6 m/s? The mass of a proton is 1.66 E-27 kg.
Remember to identify your data, show your work, and report the answer using the correct number of significant digits and units.

Answer 1

De Broglie's identity gives the relationship between the momentum and the wavelength of a particle:
$p=mv= \frac{h}{\lambda}$
where
p is the particle momentum
m is its mass
v its velocity
h is the Planck constant
$\lambda$ is the wavelength

By re-arranging the equation, we get
$\lambda= \frac{h}{mv}$
and by using the data about the proton, given in the text, we can find the proton's wavelength:
$\lambda= \frac{h}{mv} = \frac{6.63 \cdot 10^{-34} Js}{(1.66 \cdot 10^{-27} kg)(5.00 \cdot 10^6 m/s)} =7.99 \cdot 10^{-14} m$