Everything Science Grade 12

CHAPTER 12. WAVE NATURE OF MATTER 12.2

DEFINITION: De Broglie Hypothesis

A particle of mass m moving with velocity v has a wavelength λ related

to is momentum p = mv by

λ =

h

p

=

h

mv

(12.1)

This wavelength, λ, is known as the de Broglie wavelength of the parti-

cle (where h is Planck’s constant). Since the value of Planck’s constant

is incredibly small h = 6. 63 × 10 −^34 J· s, the wavelike nature ofev-

eryday objects is not really observable.

FACT

The de Broglie hypoth-

esis was proposed by

French physicist Louis de

Broglie (15 August 1892

• 19 March 1987) in
  1923 in his PhD the-
  sis. He was awarded the
  Nobel Prize for Physics
  in 1929 for this work,
  which made him the first
  person to receive a No-
  bel Prize on a PhD the-
  sis.

Example 1: de Broglie Wavelengthof a Cricket Ball

QUESTION

A cricket ball has a mass of 0 ,150 kg and is bowled towards a bowler at

40 m· s−^1. Calculate the de Broglie wavelength of the cricket ball.

SOLUTION

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

We are required to calculate the de Broglie wavelength of a

cricket ball given its mass and speed. We can do this by using:

λ =

h

mv

Step 2 : Determine what is given

• The mass of the cricketball m = 0,150 kg


• The velocity of the cricket ball v = 40 m· s−^1


• Furthermore we knowPlanck’s constant h = 6, 63 ×
  10 −^34 J· s
  Step 3 : Calculate the de Broglie wavelength