Everything Science Grade 12

CHAPTER 12. WAVE NATURE OF MATTER 12.2

Although the electron and cricket ball in the two previous exam-

ples are travelling at thesame velocity the de Broglie wavelength

of the electron is muchlarger than that of the cricket ball. This

is because the wavelength is inversely proportional to the mass of

the particle.

Example 3: The de Broglie wavelength of an electron

QUESTION

Calculate the de Brogliewavelength of a electronmoving at 3 × 105 m· s−^1.

SOLUTION

Step 1 : Determine what is required and how to approach the problem

We are required to calculate the de Broglie wavelength of an

electron given its speed. We can do this by using:

λ =

h

mv

Step 2 : Determine what is given

• The velocity of the electron v = 3× 105 m· s−^1


• The mass of the electron m = 9, 11 × 10 −^31 kg


• Planck’s constant h = 6, 63 × 10 −^34 J· s

Step 3 : Calculate the de Broglie wavelength

λ =

h

mv

=

6 , 63 × 10 −^34 J· s

(9, 11 × 10 −^31 kg)(3× 105 m· s−^1 )

= 2, 43 × 10 −^9 m

This is the size of an atom. For this reason, electrons moving

at high velocities can be used to “probe” the structure of atoms.

This is discussed in more detail at the end of this chapter. Figure

12.1 compares the wavelengths of fast movingelectrons to the

wavelengths of visible light.