Question

What is the wavelength of the matter wave associated with a proton moving at 377377 m/s? wavelength of proton matter wave: mm What is the wavelength of the matter wave associated with a 159159 kg astronaut (including her spacesuit) moving at the same speed? wavelength of astronaut matter wave: mm What is the wavelength of the matter wave associated with Earth moving along its orbit around the Sun? wavelength of Earth matter wave: m

Answer 1

1) $1.05\cdot 10^{-9} m$

The wavelength of the matter wave (also called de Broglie wavelength) of an object is given by

$\lambda=\frac{h}{mv}$

where

$h=6.63\cdot 10^{-34} Js$ is the Planck constant

m is the mass of the object

v is its velocity

For a proton, we have:

$m=1.67\cdot 10^{-27} kg$

and the velocity of this proton is

$v=377 m/s$

So, its de Broglie's wavelength is:

$\lambda=\frac{6.63\cdot 10^{-34}}{(1.67\cdot 10^{-27})(377)}=1.05\cdot 10^{-9} m$

2) $1.11\cdot 10^{-38} m$

We can use again the same equation:

$\lambda=\frac{h}{mv}$

where in this case we have:

m = 159 kg is the mass of the astronaut + spacesuit

v = 377 m/s is the velocity of the astronaut

Substituting into the equation,

$\lambda=\frac{6.63\cdot 10^{-34}}{(159)(377)}=1.11\cdot 10^{-38} m$

3) $3.70\cdot 10^{-63} m$

Similarly, we can use the same equation:

$\lambda=\frac{h}{mv}$

where in this case we have:$m=5.98\cdot 10^{24}kg$ is the Earth's mass

$v=30 km/s = 30000 m/s$ is the velocity of the Earth around the Sun

Substituting,

$\lambda=\frac{6.63\cdot 10^{-34}}{(5.98\cdot 10^{24})(30000)}=3.70\cdot 10^{-63} m$