Simple Nature - Light and Matter

equations of general validity are those that do not havecin them:

E=hf

p=h/λ

This is essentially the reasoning that de Broglie went through,

and experiments have confirmed these two equations for all the fun-

damental building blocks of light and matter, not just for photons

and electrons.

The second equation, which I soft-pedaled in the previous chap-

ter, takes on a greater importance for electrons. This is first of

all because the momentum of matter is more likely to be significant

than the momentum of light under ordinary conditions, and also be-

cause force is the transfer of momentum, and electrons are affected

by electrical forces.

The wavelength of an elephant example 11

.What is the wavelength of a trotting elephant?

.One may doubt whether the equation should be applied to an

elephant, which is not just a single particle but a rather large col-

lection of them. Throwing caution to the wind, however, we esti-

mate the elephant’s mass at 10^3 kg and its trotting speed at 10

m/s. Its wavelength is therefore roughly

λ=

h

p

=

h

mv

=

6.63× 10 −^34 J·s

(10^3 kg)(10 m/s)

∼ 10 −^37

(

kg·m^2 /s^2

)

·s

kg·m/s

= 10−^37 m

The wavelength found in this example is so fantastically small

that we can be sure we will never observe any measurable wave

phenomena with elephants or any other human-scale objects. The

result is numerically small because Planck’s constant is so small,

and as in some examples encountered previously, this smallness is

in accord with the correspondence principle.

Although a smaller mass in the equationλ = h/mvdoes re-

sult in a longer wavelength, the wavelength is still quite short even

for individual electrons under typical conditions, as shown in the

following example.

The typical wavelength of an electron example 12

.Electrons in circuits and in atoms are typically moving through

892 Chapter 13 Quantum Physics