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.

- anonymous

- Stacey Warren - Expert brainly.com

Hey! We 've verified this expert answer for you, click below to unlock the details :)

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

- anonymous

i think, the false one is 3.

- anonymous

can you tell me how???

- anonymous

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.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

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)

- anonymous

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

- anonymous

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

- anonymous

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

- anonymous

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.

- anonymous

how can all the option be correct?

- anonymous

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

- anonymous

by increasing amplitude the number of photons increases..

- anonymous

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.

- theEric

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.

- anonymous

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

- anonymous

You are not correct, I am afraid.

- anonymous

okay.. maybe m wrong..

- anonymous

@theEric u agree?

- anonymous

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.

- theEric

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.

- theEric

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!

- theEric

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

- anonymous

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.

- anonymous

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

- anonymous

awww that'x soooo confusing,....

- theEric

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?

- theEric

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.

- anonymous

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...

- theEric

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.

- anonymous

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.

- anonymous

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

- anonymous

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

- theEric

@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?

- anonymous

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.

- theEric

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

- anonymous

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

- theEric

Cool! Enjoy!

- aaronq

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

- theEric

:)

Looking for something else?

Not the answer you are looking for? Search for more explanations.