About a year ago, David, M0VTG, was reading "From Atoms to Amperes" by FA Wilson. His thoughts turned to a seasonal application of Wilson's lessons.... Thanks David!
WAVELENGTH OF SANTA AND HIS SLEIGH
We're going to need to know the
following:
Total mass of the sleigh, reindeer,
Santa and his presents, and the speed at which the sleigh travels.
Assuming that the sleigh travels relatively close to the surface of
the earth, the mass can be regarded as the same as the weight. Now
assume each reindeer weighs 100 kg. Traditionally there are nine of
them so total mass of the reindeer is 900kg. Say the sleigh also
weighs 500kg and Santa and his presents weigh 400kg; then the total
mass is 1800kg. To get round all the children who believe in him in
one night would mean him travelling at a speed of say 1000kph (277.8
m/s). (Note that scientific notation for numbers used is that used
on some calculators)
So mass (m) is 1800kg
velocity (v) is 1000kph (notice
the not so subtle change from a scalar quantity to a vector
quantity).
Max Plank came up with a formula: E
= hf relates Energy to frequency
using h (Plank's
constant = 6.626 E-34 Joule seconds).
Albert
Einstien (as everyone knows) says that E = mc2
(where c is the velocity of light).
So it
follows that hf = mc2
and
therefore, m = hf/c2.
The
momentum of a photon (p) is
defined as mass x velocity or p = mv and
as every radio amateur knows, wavelength (λ)
is the velocity of light divided by frequency or λ = c/f
(or f/c = 1/ λ).
So mv
= hf/c2 x
c (velocity of a photon is c
don't forget); so p =
hf/c
Since
f/c =1/ λ, then p =
h/λ i.e. λ =h/p
Also
since p = mv then λ
= h/mv (This expression is known
as the de Broglie wavelength - Louis Victor de Broglie)
Notice that the
velocity of light does not directly feature is the expression. We
can, therefore use it the calculate the wavelength of anything!
So the wavelength
of Santa's sleigh is Plank's constant divided by the mass times the
velocity or
λ = 6.626
E-34 J s / (1800 kg x 277.8 m/s) which equals 1.325 E-39 m - an
unbelievably small number! Make up you own mass and velocity for the
sleigh if like.
I
defy NORAD to track such a short wavelength.
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Fessenden
WA1ZMS constructed his MOPA transmitter from 1920s-vintage components. [Brian Justin, WA1ZMS, photo]
