Questions about the highest-energy photons detected

[IsItSo]

https://en.wikipedia.org/wiki/Very-high-energy_gamma_ray

Wikipedia says this about Very-High-Energy Gamma Rays:

This is approximately equal to wavelengths between 1.24 × 10−17 and 1.24 × 10−20 meters, or frequencies of 2.42 × 1025 to 2.42 × 1028 Hz. Such energy levels have been detected from emissions from astronomical sources such as some binary star systems containing a compact object.[1]

Wikipedia also says a helium atom is 62 picometers across essentially.

1st question:
Of the photons detected, how small in picometers is the shortest wavelength photon?

I need to know how many "fit" within an atom. These photons have got to be at least as small as quarks.

2nd question:
I don't understand why "1.24" is in front of "× 10−20 meters". Do they mean a 0.2 with 20 0s after it? Times 1.24?

3rd question:
And lastly the frequency, "2.42 × 1028 Hz", shouldn't this number be double the wavelength? And how do they know its frequency - do they register each "hit" within 1 second?

 

[Nugatory]

1st question:
Of the photons detected, how small in picometers is the shortest wavelength photon?

Like the article says (but see the second question below), ##1.24\times{10}^{-20}## meters, which is ##1.24\times{10}^{-8}## picometers. However, you should be aware that photons are not small objects that occupy some definite volume, the wavelength isn't the size of anything, and any notion of trying to "fit" some number of photons into an atom is going to be seriously misleading.

2nd question:
I don't understand why "1.24" is in front of "× 10−20 meters". Do they mean a 0.2 with 20 0s after it? Times 1.24?

They mean ##1.24\times{10}^{-20}## meters... but they also say "between ##1.24\times{10}^{-17}## and ##1.24\times{10}^{-20}## meters", and providing three significant digits when they're unsure by a factor of 1000 what the actual value is is absurd. They should say "somewhere between about ##{10}^{-17}## and ##{10}^{-20}## meters", and leave it at that.

3rd question:
And lastly the frequency, "2.42 × 1028 Hz", shouldn't this number be double the wavelength? And how do they know its frequency - do they register each "hit" within 1 second?

The wavelength and the frequency are related by ##\lambda\nu=c## where ##\lambda## is the wavelength, ##\nu## is the frequency, and ##c## is the speed of light. You can visualize this if you imagine ##\nu## peaks moving at the speed of light passing by every second, each separated by the wavelength ##\lambda##.

We know the frequency because we've measured the energy, and the frequency can be calculated from the energy using ##E=h\nu## where ##h## is Planck's constant.

 

[IsItSo]

But am I supposed to times 10-20 by 1.24? Why don't they just give the answer/number? It's not a solid number, ex. 5, it's an equation ex. 5 x 99.

 

[DrClaude]

But am I supposed to times 10-20 by 1.24? Why don't they just give the answer/number? It's not a solid number, ex. 5, it's an equation ex. 5 x 99.

It's called scientific notation, and it is very useful when dealing with very big or very small numbers. If you want to express a length of 1.24 pm in meters, it is very cumbersome to always have to write 0.00000000000124 m, and very difficult to read. So you separate the powers of 10, and write 1.24 × 10^-9 m.

 

[IsItSo]

How do they calculate a photons wavelength? I know what yous say all the time, but, isn't the full proof way to calculate this by seeing if it goes through a hole to determine its size? Determining its energy is one thing, but talking about "wavelength" only makes sense to me if they know how big it is function-ing-ly acting most of the time.

 

[Nugatory]

How do they calculate a photons wavelength? I know what yous say all the time, but, isn't the full proof way to calculate this by seeing if it goes through a hole to determine its size? Determining its energy is one thing, but talking about "wavelength" only makes sense to me if they know how big it is function-ing-ly acting most of the time.

All photons with the same energy have the same frequency and wavelength, so determining anyone of those three quantities is sufficient to determine all three. It's like with a circle: If you've measured anyone of the radius, diameter, and circumference, you don't need to measure the other two to know what they are.

 

[mfb]

isn't the full proof way to calculate this by seeing if it goes through a hole to determine its size?

The wavelength is not a "size of a photon" - there is no such thing (or 0, depending on how you want to view it). Electromagnetic waves with a wavelength of many meters can easily enter your room through the windows, for example.

 

[IsItSo]

Ok...but...why use meters then....the wiki page says a picometer is 1 trillionth of a meter.

 

[mfb]

Why use picometers if you still need the scientific notation because it is so much smaller than a picometer?

With meters, unit conversions are easier.

 

[IsItSo]

Yes, you can say either it's 1 trillionth of a meter or 1 picometer, BUT, in either scenario, it's still saying that the photon is 1-trillionth of a meter! Why say this! It has to be 1 trillionth of a meter.

 

[Nugatory]

Ok...but...why use meters then....the wiki page says a picometer is 1 trillionth of a meter.

We use meters because if we use one unit everywhere life gets easier. The relationship between frequency and wavelength is given by ##\lambda\nu=c##. We know the frequency ##\nu## from the energy, so all we need to do is google for the value of ##c## and we'll know everything we need to calculate the wavelength... And we when we do google for the value of ##c##, we get many many hits saying that it is ##3\times{10}^8## meters per second. So we plug the frequency ##\nu## and this value of ##c## into ##\lambda\nu=c##, and out pops our answer in terms of meters: the wavelength ##\lambda## is between ##10^{-17}## and ##10^{-20}## meters depending on what the energy was. We could look for an answer in terms of picometers, but then we'd have to do an extra step, dividing the distance in meters by ##10^{12}## to convert it into picometers. Now we have something between ##10^{-5}## and ##10^{-8}## picometers, but we had do an extra step and we don't know anything that we didn't already know when we had the answer in meters.

So generally we want to pick one unit for length and one unit for time and then use those everywhere. As long as the convention is to provide the value of ##c## (needed to relate frequency and wavelength) and ##h## (needed to relate energy and frequency) using meters as the unit of distance, we might as well use meters everywhere. Choosing other units just makes us do extra and unnecessary multiplications and divisions.

 

[IsItSo]

No what I meant is, when you say "this photon X" is a trillionth of a meter or 1 picometer, saying such is suggesting the photon is that small, i.e. that-much-of-a-meter, because either way you say it is 1 trillionth of a meter or that it's 1 picometer - a trillionth of a meter. The photon must be that small. Why else would you say it is that-much-of-a-meter.

 

[ChrisVer]

No what I meant is, when you say "this photon X" is a trillionth of a meter or 1 picometer, saying such is suggesting the photon is that small,

A photon does not have a wavelength, neither is it small or big (at current knowledge photons are point-like particles).

 

[DrClaude]

when you say "this photon X" is a trillionth of a meter or 1 picometer,

The point is that nobody is saying that. What is said is that the photon's wavelength is 1 pm. In other words, as it travels at the speed of light, the distance between two consecutive peaks of the electromagnetic field is 1 pm. It says nothing about the size of the photon.

 

[IsItSo]

Aren't photons dual-theory i.e. wave-like particle-like?

 

[ChrisVer]

Aren't photons dual-theory i.e. wave-like particle-like?

1st, if you consider it as a wave then you wouldn't speak of size since a wave expands everywhere.
2nd, I think you mix the wavelikeness with something else. The electron for example is not a wave. The probability density of the electron (the information you can get out of a Quantum-mechanical treatment of the problem) behaves like a wave, that renowned Schrodinger's [itex]\psi[/itex].
3rd, photons themselves are the particles, excitations of the photon field [that expands throughout the whole space].

 

[IsItSo]

I don't think that makes total sense...try again...

Also if radio is so big that how is that point-like-particles?

 

[mfb]

Also if radio is so big that how is that point-like-particles?

The spread of the wave is not a particle size. This has been said multiple times now.

 

[IsItSo]

Are you saying that the photon is a point-like-particle, while it caries a wave ball? Like a massive city-sized glass ball with a hard dark point-particle in its center?

Or that the point-like-particle is moving uppp and downnnn repeat in a big radio wave as wide as a city? How does that cover 3 dimensions.

 

[ChrisVer]

Are you saying that the photon is a point-like-particle

yes.

while it caries a wave ball?

What is a wave ball? You could rephrase the question in a nicer manner (look my last line). This thread is B-labeled afterall and can't go too deep into details [though nobody is trying to lead you astray].

Like a massive city-sized glass ball with a hard dark point-particle in its center?

Are you mistakening there light (electromagnetic waves) with photons?

Or that the point-like-particle is moving uppp and downnnn repeat in a big radio wave as wide as a city?

photons don't move up and down. Photons move in "straight" lines. Nothing moves up and down for light propagation (that even happens in vacuum), the electric and magnetic fields are oscillating.

In general, It would be better if you were asking questions nicely.

 

[IsItSo]

I didn't think my reply was rude... I'm sorry.

I am pretty lost, now.

Aren't the radio-photons big? As big as a city? At least I mean, something about them is, from what I read before.

 

[ChrisVer]

I didn't think my reply was rude... I'm sorry.

well then I guess I misinterpreted the way you wrote your question.

Aren't the radio-photons big? As big as a city?

the radio-waves (not photons?) are as big as a city = their wavelength is as big as a city. Again I think you should resolve your confusion between light and photons... wavelength though is not a "size" of something, it tells you the distance between two points that have the same oscillation amplitude...

 

[mfb]

As long as you think of light as a stream of particles moving around, you won't get a clear picture. Photons don't even have a position. You try to use concepts from classical mechanics for something that can only be described properly with quantum mechanics. That cannot work.