Modern Physics

Matter Waves

de Broglie's hypothesis and the wave behavior of particles

Matter Waves lesson illustration

Can electrons passing through 2 slits
produce an interference pattern?

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Wave Nature of Electrons
- whatthebleep.com

 

Show Me The Physics
YouTube Channel

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Fill In the Blank Notes

 

D) Matter Waves - ALL moving particles have wave properties.

Louis de Broglie timeline showing his matter-wave hypothesis, Nobel Prize, and contributions to quantum mechanics
Louis de Broglie
λ = h/p = h/mv

 

 

p = momentum of the particle

λ - called DeBroglie Wavelength

h - Planck's constant

 

 

 

The wavelength of ordinary objects are insignificant because
their masses are too large.

 


BUT…

 

 Electrons are small enough

to have a significant
wave behavior.

 

 

 

 

1927- Diffraction and interference patterns were observed for electrons.

 

 

A scientist passed electrons through tiny double slits and observed interference patterns

 

Where did they get slits small enough
 and close enough?

Matter Waves lesson illustration

 

 

Pattern produced when a beam of

electrons pass through a double slit

Matter Waves lesson illustration

 

When you pass a beam of electrons through the slits of a crystal you get an interference pattern

 


 

 

Final Summary

  

IS LIGHT A WAVE OR A PARTICLE?

 

 

Matter Waves lesson illustration

 

 

 
Light behaves like a
wave in interaction
with large objects

and like particle with very small objects
 like electrons

 

 

 

Matter Waves lesson illustration

 

- Douglas Hofstadter

 


 

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. According to de Broglie, which objects have wave properties?

2. The de Broglie wavelength of a particle is given by…

3. An electron's speed is doubled. What happens to its de Broglie wavelength?

4. Why don't we notice the wave behavior of a thrown baseball?

5. What 1927 observation confirmed that electrons behave like waves?

NYSSLS Regents Practice · Modern Physics · Matter Waves

The Electron Microscope

In 1924, Louis de Broglie proposed that moving particles have a wavelength, λ = h ÷ mv. Electron microscopes use fast electrons instead of light. An electron (m = 9.11 × 10−31 kg) moves at 1.0 × 106 m/s. (h = 6.63 × 10−34 J·s)

What is the electron’s de Broglie wavelength?

▶ Want a challenge? Open 6 more Regents-style questions  (harder · mixed formats)

Challenge score: 0 / 6

Multiple choice

C1. Why can electron microscopes see much finer detail than light microscopes?

Substitute values

C2. A proton (m = 1.67 × 10−27 kg) moves at the same speed as the electron, 1.0 × 106 m/s. Substitute numerical values into a mathematical representation that can be used to determine the proton’s de Broglie wavelength. Then calculate it.

λ = ( × 10−34 J·s)( × 10−27 kg)( × 106 m/s) = × 10−13 m
Support or Refute · Justify

C3. A student makes the following claim.

Claim: An electron microscope that uses electrons moving at 2.0 × 106 m/s can resolve finer detail than one that uses electrons moving at 1.0 × 106 m/s.

Place a check mark in either the Support or Refute box. Justify your response using a mathematical relationship.

Determine the value

C4. To image a crystal, an engineer wants electrons with a de Broglie wavelength of 1.0 × 10−10 m. Determine the speed the electrons must have. Enter the number that goes in front of × 106 m/s.

v = × 106 m/s
Multiple choice

C5. Which experiment provided evidence for matter waves?

Constructed response

C6. An engineer plans to increase the electron speed in a microscope to produce sharper images. Identify one benefit and one drawback of this design change.

Early Models of the Atom →

Also see: The Big Bang — evidence for the origin of the universe

Also see: Nuclear Physics — radioactive decay, fission, and fusion