Question

Which of the following statements is false regarding electromagnetic waves ?

If the amplitude of em waves in a monochromatic beam of light is increased, then

1. The energy transported by the beam will increase.

2. The pressure exerted by beam will increase.

3. The number of photons will increase.

4. The momentum of photons will increase.

Answer 1

i think, the false one is 3.

Answer 2

can you tell me how???

Answer 3

No, the correct answer is 4. The energy and momentum of the photon depends on the frequency of the radiation. A higher wave amplitude corresponds to a greater intensity, or more photons, but not an increase in the energy of each photon.

Answer 4

As i know, the EM wave energy is proportional to the square of E or B field. And also photon momentum is proportional its energy. P=E/c (where E is energy not E field)

Answer 5

Are you agreeing or disagreeing? I can't tell.

Answer 6

i think the false one is option 1.
wt u say @aaronq ??

Answer 7

energy depends on frequency , not intensity, by increasing intensity we are increasing number of photons...

Answer 8

The energy carried by a classical electromagnetic wave is proportional to the square of the amplitude of the electric field. Option A is correct.

The pressure exerted by a classical electromagnetic wave is related to its intensity. Option B is correct also.

The number of photons travelling through space is related to the energy carried by the corresponding classical electromagnetic wave, so option C is correct as well.

Answer 9

how can all the option be correct?

Answer 10

wait , wait...
option c isn't correct @Jemurray3

Answer 11

by increasing amplitude the number of photons increases..

Answer 12

I meant those statements are correct. The question wants to know which one is false -- so the answer to the question is that the last option, number 4, is a false statement.

Answer 13

The energy of one photon is \(E=hf\), where \(h\) is Planck's constant and \(f\) is frequency.
The momentum of one photon is \(p=\dfrac{h}{\lambda}\), where \(\lambda\) is wavelength.
Pressure depends on the change in momentum per time (force) and the area where you consider the pressure to be.
http://en.wikipedia.org/wiki/Photon

The number of photons is the number of energy "packets." The total energy of the photons has some proportionality to the the amplitude of the wave, but I'm not sure what that proportion is. In monochromatic light, meaning one color or one wavelength, each photon has the same energy. The number of photons, then, is the total energy divided by the energy of that one wavelenth.

Answer 14

nopx option 1 is false.. as far as i know..

Answer 15

You are not correct, I am afraid.

Answer 16

okay.. maybe m wrong..

Answer 17

@theEric u agree?

Answer 18

The energy transported by the wave is given by the Poynting Flux, which is proportional to the square of the amplitude of the electric field.

Answer 19

If (3) is true, as we agree, then so must be (1). Each photon has so much energy. More photons would carry a total of more energy.

Answer 20

So I would think that (2) is also true, since more photons means more momentum affecting an area. Then (4) remains. The total momentum will increase, but the momentum of each is only related to the wavelength. Weird wording!

Answer 21

If only the amplitude of the wave is increased, we know it can only be more photons.

Answer 22

It's not weird wording. That's the correspondence between classical EM waves and photons -> amplitude of the field has NOTHING to do with the energy/momentum of each individual photon, which was encapsulated in the photoelectric effect, which was one of the things that gave rise to the idea of photons in the first place.

Answer 23

It might be a weird effect, but that's the way it goes.

Answer 24

awww that'x soooo confusing,....

Answer 25

Weird wording:
"The momentum of photons will increase."
It could have been, "the momentum of each photon will increase."

The total momentum, which is the momentum of the photons [combined], will increase.

Do you disagree?
\[p_\text{total}=\Sigma_{i=1}^n \ \ p_i\] where the subscript of \(i\) represents a unique label for each photon?

Answer 26

Photons are distinct energy packets. There were photons that released electrons that could be freed from their atoms. They realized the enery came from frequency, because that is what gave the electrons the energy to free themselves. The energy of the electrons released would also be due to frequency, not so much how many protons you threw at the electrons. There's more to it, but that's part of it.

Answer 27

I've never heard anybody talk about the total momentum of an electromagnetic wave but I guess so. As worded, the "total momentum" of the wave doesn't make sense because there'd be an infinite number of photons. If you wanted the total momentum you'd need to know how long the wave was, etc...

Answer 28

And I believe Albert Einstein created the theory to describe photoelectric effect, and we still use that theory. The effect, though, was known for some time before that. Yay, Einstein!

And, I don't think there would be infinite photons. Would there be? Maybe over an infinite period of time.... Assuming there was infinite energy or it was recycled. I wonder if time could be recycled :P But it really wouldn't be infinite, right? But I'm not smart enough to back up that thought, and also I can't prove it, certainly.

Answer 29

There would only be an infinite number of photons in monochromatic beam if it was going on forever -- but that's pointless to talk about, so normally you just refer to the momentum of each photon individually. Multiplying that by the rate at which photons strike a surface will give you the force on that surface.

Answer 30

increasing intensity means increasing number of photons , not the energy of photons ...

Answer 31

Or half the force, in the case of a reflective surface.... and yes, that's right.

Answer 32

@KhiZ yeah, greater amplitude, in the way we're looking I guess, doesn't increase the energy of each photons. But (1) makes the wording to show that it is the energy carried by the wave, which is the sum of the photons.

@Jemurray3 I guess the proportion of the force would depend on the reflectivity of the material, is that right? Also, a wave that has an infinite length must have taken an infinite amount of time to propagate, since even light has a limiting speed, right? But, mathematically, the theoretical can be described in numbers. So I can believe it is a convention to express a wave with an equation that makes it infinitely long.. But that would be theoretical, right?

Answer 33

Yes, it would depend on the reflectivity, and yes of course it's impossible to realize physically but mathematically it's how we model it.

Answer 34

Cool, thanks! :) Very much! Good conversion! It was educational, thanks all! :) And I will continue to look at this post for more replies, haha!

Answer 35

this question made me curious...
i'll discuss it with my phy teacher ..
bye...

Answer 36

Cool! Enjoy!

Answer 37

i agree! "The momentum of photons will increase" is false.

Answer 38

:)