Share with your friends
Call

$lambda = 1.1 xx 10^(-38) "m"$


The de Broglie wavelength $lambda$ in $"m"$ is given by the de Broglie relation:

$lambda = h/(mv)$

where:

  • $h = 6.626 xx 10^(-34) "J" cdot"s"$ is .
  • $m$ is the mass of the mass-ive object in $"kg"$.
  • $v$ is its velocity in $"m/s"$.

The units here are wacky, so we'll need to convert the $"lb"$ into $"kg"$ and the $"mph"$ into $"m/s"$. We have the following conversion factors to consider:

$"2.2 lb"/"kg"" "" "" ""5280 ft"/"1 mi"" "" ""12 in"/"1 ft"$

$"2.54 cm"/"1 in"" "" ""100 cm"/"1 m"" "" ""60 min"/"1 hr"$

$"60 s"/"1 min"$

First, convert the mass:

$5400 cancel"lbs" xx "1 kg"/(2.2 cancel"lbs") = "2454.5 kg"$
$" "" "" "" "" "" "" "" "$(we'll round later)

Now convert the velocity:

$(57 cancel"mi")/cancel"hr" xx (5280 cancel"ft")/(cancel"1 mi") xx (12 cancel"in")/(cancel"1 ft") xx (2.54 cancel"cm")/(cancel"1 in") xx "1 m"/(100 cancel"cm") xx (cancel"1 hr")/(60 cancel"min") xx (cancel"1 min")/("60 s")$

$=$ $"25.481 m/s"$
(we'll round later)

Lastly, just solve the de Broglie relation for the wavelength.

$color(blue)(lambda) = (6.626 xx 10^(-34) cancel"kg" cdot"m"^cancel(2)"/"cancel"s")/(2454.5 cancel"kg" cdot 25.481 cancel("m/s"))$

$= ulcolor(blue)(1.1 xx 10^(-38) "m")$

And this number is justifiably puny.

A macroscopic particle like a sports utility vehicle has practically no wave characteristics to speak of. Only really light particles moving at very fast speeds are quantum mechanical.

Talk Doctor Online in Bissoy App