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### Wave-Particle Duality

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• Question 1 0:15
• Question 2 0:34
• Question 3 0:53
• Question 4 1:54
• Question 5 2:16
• Question 6 2:27
• Question 7 2:42
• Question 8 2:59
• Question 9 3:45
• Question 10 4:13
• Question 11 4:33

### Transcription: Wave-Particle Duality

Hi everyone and welcome back to Educator.com.0000

In this mini-lesson, we are going to go through page 1 of the APlusPhysics worksheet on wave particle duality.0002

You can find the link to that worksheet down below the video.0008

Let us dive right in.0012

As you do this, you are probably going to need a copy of the electromagnetic spectrum near you in order to answer the questions.0013

Number 1 -- Compared to a photon of red light, a photon of blue light has a...?0019

Blue has a greater energy than red light. It has a higher frequency, therefore it has a higher amount of energy -- Number 1.0024

Number 2 -- Exposure to UV radiation can damage skin and exposure to visible light does not damage the skin.0035

State one possible reason for this difference.0041

UV radiation has more energy because it has a higher frequency.0043

Number 3 -- Louis de Broglie extended the idea of wave particle duality to all of nature with his matter wave equation, λ equals Planck's constant divided by mass times velocity, where λ is the particles wavelength, (m) is its mass, (v) is its velocity and (H) is Planck's constant.0053

Using this equation, calculate the de Broglie wavelength of a helium nucleus moving with a speed of 2 × 106 m/s.0069

If λ equals h/mv, that is going to be...0077

...well Planck's constant is 6.63 × 10-34/6.7 × 10-27 kg (mass) divided by 2 × 106 m/s (velocity) is going to give us a wavelength of about 4.95 × 10-14 m.0083

That is a pretty, pretty, pretty, really, really, really small wavelength.0108

Number 4 -- The wavelength of this particle is of the same order of magnitude as which type of electromagnetic radiation?0114

To do that I need to go to the electromagnetic spectrum where I find that that is very close into the realm of gamma rays.0120

Number 5 -- A photon of light carries -- well it carries both energy and momentum -- correct answer there is Number 3, photons have energy and momentum, but no mass.0136

Number 6 -- Wave particle duality is most apparent in analyzing the motion of small, small particles -- baseball, space shuttle, galaxy -- all big, but an electron is small, so this is most apparent for the electron.0147

Number 7 -- A photon of which electromagnetic radiation has the most energy?0162

Well, it is going to be the one with the highest frequency.0166

UV, x-ray, infrared, or microwave -- I will use the electromagnetic spectrum diagram to see that that is going to be Number 2, x-ray.0168

Number 8 -- Light of wavelength 5 × 10-7 m consists of photons having what energy?0179

To do this, energy is going to be equal to HF or HC/λ using the wave equation where V = F(λ) and our velocity is C.0185

So that is going to be 6.63 × 10-34 × 3 × 108 m/s (c, the speed of light in a vacuum)/5 × 10-7 m (wavelength)...0198

...which is going to give us an energy of right about 4 × 10-19 J -- Answer Number 3.0211

Number 9 -- Electrons oscillating with a frequency of 2 × 1010 Hz produce electromagnetic waves.0225

These waves would be classified as...?0232

Well, if they oscillate at that frequency, the waves created would have a frequency of 2 × 1010 Hz as well.0234

Using the electromagnetic spectrum, I can look and find out that those fall into the range of microwaves -- Answer Number 3.0242

Number 10 -- The energy of a photon is inversely proportional to its...?0253

Now remember energy is (HF) or HC/λ, so wavelength -- Yes, it is inversely proportional to wavelength, so the answer must be Number 1.0258

Last question -- A photon has a wavelength of 9 × 10-10 m.0273

Calculate the energy of this photon in joules.0278

Well, again, energy is HC/wavelength, which is going to be 6.63 × 10-34 (Planck's constant) × 3 × 108 m/s (the speed of light in a vacuum)/9 × 10-10 m (wavelength).0281

I plug that into my calculator and I come up with something pretty close to 2.2 × 10-16 J.0300

That completes the first page of the worksheet on wave particle duality. If you struggled with this, it is probably time to go back and review that lesson in the main portion of our lecture series.0311

If it went great -- Excellent -- Time to move on.0324

Thanks so much for your time everyone and make it a great day.0327