Physical Chemistry Third Edition

15.1 De Broglie Waves 655

As assumed by de Broglie

(a)

Mismatch–contrary to assumption

(b)

Figure 15.1 De Broglie Waves around a Closed Orbit.(a) An integral number of

wavelengths on the circumference. (b) Not an integral number of wavelengths on the

circumference.

de Broglie presented his doctoral dissertation containing this proposal, the examining

committee accepted the dissertation but refused to believe that it corresponded to phys-

ical reality. The wave nature of ordinary objects is not observable because of the small

wavelengths that occur.

EXAMPLE15.1

Calculate the de Broglie wavelength of a baseball of mass 5.1 oz thrown at 95 miles per hour.

Solution

λ

6. 6261 × 10 −^34 Js

(5.1oz)(95mih−^1 )

(

16 oz

11b

)(

11b

0 .4536 kg

)(

3600 s

1h

)(

1mi

1609 m

)

 1. 1 × 10 −^34 m

The smallness of this value suggests why matter waves are not observed for baseballs.

The mass of electrons is so small that de Broglie suggested at his final oral

examination that electron diffraction by crystals could verify his theory. In 1927,

Davisson and Germer^2 accidentally grew a single crystal while heating a piece of

nickel. When they irradiated this nickel crystal with a beam of electrons, they observed

diffraction effects, verifying the existence of de Broglie’s matter waves.

Exercise 15.1

Find the speed of electrons with a de Broglie wavelength equal to 2.15× 10 −^10 m, the lattice

spacing in a nickel crystal.

(^2) C. J. Davisson and L. H. Germer,Phys. Rev., 30 , 705 (1927).