Can the Energy of a Photon be Expressed in h/s?

[bobie]

Hi,

Energy is expressed in J or eV, but E= hf
As Planck constant h is J.s is it possible to express the energy of a photon in h/s? If not, why?
Can we say that the energy of a photon is 2.41 x 10^14 h/s?

 

[Drakkith]

If h = Js, then J = h/s, and you can express E in joules, so it appears to me that you are already using h/s.

 

[Naty1]

E = hf shows photon energy [E] varies with frequency [f].

Your proposal does not.

Your proposal is missing a unit of measure.
For some unit relationships, try

http://en.wikipedia.org/wiki/Planck_constant

 

[bobie]

Your proposal is missing a unit of measure.

What unit is missing?
A photon with frequency 2.418 x 10^14 Hz has E = 1 eV, is that correct?
h = 4.135 x 10 ^-15 eV.s , h/s = 4,135 x 10^-15 eV (from your link)
( 2.318x 10^14 x) h/s = (2.428x10^14 x) 4.135 x 10^-15 eV
2.318x 10^14 x h/s = 1
A photon with frequency 2.418 x 10^14 Hz has E = 2.418 x 10^14 h/s

Where do I go wrong?

 

[Naty1]

Can we say that the energy of a photon is 2.41 x 10^14 h/s?

'h' is a constant, right?

What does 's' mean in your equation?? Please explain.

 

[DennisN]

Can we say that the energy of a photon is 2.41 x 10^14 h/s?

Be careful here, you are mixing a constant (h) and a unit (s) in the same unit expression, which is very unusual and should be avoided IMO.

You obviously mean

h: Planck's constant ≈ 6.626×10⁻³⁴ J·s (joules times seconds)
s: seconds

but h as a unit usually mean hour. The usual unit - the SI unit - of energy is the joule (J), not any h/s. There are also some other units of energy like the electronvolt (eV).

Hmm... I'm wondering if someone will give me a prize for using the most wikipedia links in one and the same short post...?

 

[bobie]

Thank you all,
If I got it right, h = J.s cannot be modified to h/s =J.
But I read that the Hz is equivalent to 1/s, then in the formula E= h.f => E = h. 1[]/s = aren't we mixing a constant with a unit?

 

[Bandersnatch]

For clarity's sake let's use brackets when we mean units, and remember to not mix the bracketed bits with unbracketed ones.

f=1/T not [1/s]
[1/s] is the unit of f

So, E=hf and the units are h=[J*s] and f=[Hz]=[1/s]

Then E=[J*s*Hz]=[J*s/s]=[J]

 

[bobie]

Thanks, if h/s is forbidden, how can we express that the scalar of the frequency is always equal to the scalar of the energy of a photon?

 

[Bandersnatch]

Not sure what you mean. Energy equals frequency of the wave times the Planck constant E=hf. These are all scalar quantities.
You can substitute 1/T for f if you like, to get E=h/T, where T is the period of the wave.

 

[bobie]

You can substitute 1/T for f if you like, to get E=h/T, where T is the period of the wave.

So , what is the E of a photon with frequency 2.418x 10^14 wxpressed in h/T?

 

[Bandersnatch]

It's the same as with the energy expressed as hf. The energy of the photon does not change just because you use some arithmetic to rearrange the equation. h/T is, after all, equal to hf in both value and units.

f=2.418*10^14 [Hz]

E=fh=2.418*10^14 [Hz]*6.626×10^-34 [J*s]=~16*10^-20 [J]

T=1/f
T=1/(2.418*10^14) [1/Hz]
T=~0.41*10^-14

E=h/T=6.626×10^-34 [J*s]/0.41*10-14 =~16*10^-20 [J]

 

[Naty1]

Just came back...
bobie,
my post #5 was an attempt to get you to see for yourself the difference between a measure, such as a frequency, f, and the unit utilized to express it, such a cycles per second.
I think that's what the prior posters are explaining,too.

If you write out the UNITS associated with any measure, any formula, you will see whether you have consistency:

for example distance equals velocity times time, right?? :
a distance = ft/sec x seconds = ft and that makes 'sense'...the seconds cancel...if you have instead a measure of speed such as [50] miles/hour x [25] seconds your units become mile-second/ hours...not a standard set of units...so much better to convert the right hand side to either hours, seconds, or whatever...


Note also the unit 'Hertz' [and seconds] has some confusion associated with it:

http://en.wikipedia.org/wiki/Cycle_per_second

[I wasn't even aware of this supposed confusion til I just checked. ]

 

[jtbell]

how can we express that the scalar of the frequency is always equal to the scalar of the energy of a photon?

We could define a new unit of energy: 1 bobie = 4.135 x 10^-15 eV = 6.626 x 10^-34 J. Give it the symbol 'B'. (Or is there another unit with that symbol? I forget...)

Then Planck's constant would be 1 B.s, and a photon with frequency 2.418 x 10¹⁴ Hz would have an energy of 2.418 x 10¹⁴ B.

 

[bobie]

We could define a new unit of energy: 1 bobie = 4.135 x 10^-15 eV = 6.626 x 10^-34 J. Give it the symbol 'B'. (Or is there another unit with that symbol? I forget...)

Then Planck's constant would be 1 B.s, and a photon with frequency 2.418 x 10¹⁴ Hz would have an energy of 2.418 x 10¹⁴ B.

Congrats, jtbell, you hit the nail on the very head!, thanks.
That's exactly what I meant without aspiring to have a unit named after me., that would make patent the relation of energy to a single oscillation (I posed a similar problem here :https://www.physicsforums.com/showthread.php?t=712514 , it seemed to me that dimensions prevent seeing the forest because of the trees. There I discovered geometrized units and that dimensions are not indispensable).
I have little (or no) experience and I still cannot see the subtle difference between 1B and 1 h/s.

Actually I cannot even grasp what a unit of energy can actually mean when multiplied by time.
I understand that power (J/s ) is energy absorbed every second but J.s would correspond to distance ( as compared to velocity, right)?

 

[dauto]

J.s is the unit for action (and also angular momentum).

 

[bobie]

J.s is the unit for action (and also angular momentum).

Can 2 different entities have the same dimensions?, what has h in common with angular momentum?

...if h indeed is a unit then it can be mixed with other units and we can use h/s?

 

[Bandersnatch]

Stop it right now, mister! Stop saying that h is a unit, or I'm going to reach through the screen and give you a good spanking!
It is most emphatically not. Nobody has ever said that. It's a constant and it's units are J*s.

h/s is mixing constants with units.
Write J*s/s if you must, although it's obviously just J, if you want to write units. Or write h/T if you want equations. Don't write h/s. It's like writing a=V/s or F=kg*a.

 

[bobie]

Stop saying that h is a unit, ...Nobody has ever said that

Why do you blame, me, bandersnatch,did you see that I was simply quoting Mr dauto, ?
how can I possibly know who is right or wrong?

 

[Bandersnatch]

Where, oh, where did he say h is a unit? All he said is that J*s is a unit.

 

[bobie]

Where, oh, where did he say h is a unit? All he said is that J*s is a unit.

Sorry, if I misunderstood, but I thought that h=J.s? wiki:
h = 1.054571726(47)×10−34 J·s
. Can two different units have same dimensions?

 

[DennisN]

Why do you blame, me, bandersnatch,did you see that I was simply quoting Mr dauto, ?
how can I possibly know who is right or wrong?

You were not quoting dauto. Dauto said:

J.s is the unit for action (and also angular momentum).

which only was about the unit [Js]. But you said:

...if h indeed is a unit then it can be mixed with other units and we can use h/s?

No, please read my post #6 again. Planck's constant (h) is not a unit, it is a physical constant (which is a physical quantity).

It seems to me that you don't understand the difference between a quantity and a unit. I think the posters in this thread have tried to explain this in various ways. But I will try to visualize it in this basic way:

Planck's constant is (full expression)

h ≈ 6.62606957 × 10⁻³⁴ Js

h is a quantity (a constant)
6.62606957 × 10⁻³⁴ is the value
Js is the unit (joules times seconds)

Is this clear? Do you understand that h is not a unit in itself, and therefore it should not be a part of a unit expression?

 

[bobie]

h is a quantity (a constant)
6.62606957 × 10⁻³⁴ is the value
Js is the unit (joules times seconds)

Is this clear? Do you understand that h is not a unit in itself, and therefore it should not be a part of a unit expression?

Thanks for your patience, I'll try to make myself clear.
T time is not a unit, is a dimension , sec is its unit
Length is not a unit , cm is its unit...
is that right?
if h is only a constant, a quantity , a value, therefore a dimensioneless number, why is it always associated to units such as J.s, dimensions?
α is the fine structure constant and is just a quantity 0.007... but is never associated to units

That is what I do not understand, when I think of h I think of α, where do I go wrong?

 

[DennisN]

Thanks for your patience, I'll try to make myself clear.

Excellent, no problem! I think we are going somewhere now:

T time is not a unit, is a dimension , sec is its unit

Yes.

Length is not a unit , cm is its unit...

Yes (though normally the unit is m (meter)).

is that right?

Yes!

if h is only a constant, a quantity , a value, therefore a dimensioneless number, why is it always associated to units such as J.s, dimensions?

This is where you go wrong (my bolding in your quote). h is not dimensionless;

Planck's constant is (full expression) h ≈ 6.62606957 × 10⁻³⁴ Js

h is a quantity (a constant)
6.62606957 × 10⁻³⁴ is the value
Js is the unit (joules times seconds)

A dimensionless quantity is a quantity without a unit. But the unit of h is Js, so h is not dimensionless.

 

[bobie]

h ≈ 6.62606957 × 10⁻³⁴ Js

So, if I got it right some constants are dimensioneless and some have units. And we have to create a new unit B to express what I meant by h/s. What would then be the relation of h to B?

Moreover, you have used a new sign ≈, and that makes more sense even if I do not know its properties: what fooled me is that wki has
h = ...J * s
and I am naive enough to think that you can always move around entities from left to right.
But the main problem remains that I have no clue what energy multiplied by time can represent.

 

[Bandersnatch]

bobie, have a look at this book:
http://old.iupac.org/publications/books/gbook/green_book_2ed.pdf

It's very informative, and an easy read. Chapter 1 covers the basic definitions and ideas behind quantity calculus. There's also a lot of tables explaining various relationships, derivations and definitions. It has probably all you'll ever need to know about units.

 

[bobie]

Thanks, that is very helpful indeed

 

[DennisN]

So, if I got it right some constants are dimensioneless and some have units.

Correct!

Moreover, you have used a new sign ≈, and that makes more sense even if I do not know its properties: [...]

Sorry if I confused you, I am accustomed to use ≈ (which means approximately equal to) to emphasize that the value is not exact. The value of Planck's constant (h) is not exactly known down to an arbitrary number of digits.

what fooled me is that wki has
h = ...J * s

Wiki says

h = 6.62606957(29)×10⁻³⁴ Js

which also is ok since the two digits inside the parentheses denote the standard uncertainty in the last two digits of the value (link), which also indicates that the value is not exact.

 

[bobie]

So, if I got it right some constants are dimensioneless and some have units

.
Correct!

Could you give me some examples of constants with units so that I can get in the picture?

 

[Bandersnatch]

Could you give me some examples of constants with units so that I can get in the picture?

In the book I linked you to, go to chapter five, or here, or http://www.ligo.caltech.edu/~vsanni/ph3/ToolsTables/NISTPhysicalConstants.pdf. You'll notice that nearly all of them have units.

 

[DennisN]

Could you give me some examples of constants with units so that I can get in the picture?

Sure! I'll also give some dimensionless constants, so we can see the difference better.

Mathematical constants (which are dimensionless):

pi (the ratio of a circle's circumference to its diameter)
e (the base of the natural logarithm)

Physical constants that are dimensionless:

α: the fine-structure constant
μ: the proton-to-electron mass ratio

Physical constants that are not dimensionless:

h: Planck's constant
c: speed of light in vacuum
G: gravitation constant
e: the elementary charge
k_e: Coulomb's constant
m_e:the mass of the electron
m_p:the mass of the proton
etc.
etc.

To see these constants (and some more) and their units, see: Fundamental Physical Constants (HyperPhysics).

 

[BruceW]

I don't see the problem with using $h$ (or $\hbar$) as a unit. For example, the orbital angular momentum of an electron in the 'p subshell' is given by: $L=\sqrt{2} \hbar$ hmm. I guess here you guys would say that the equation is simply comparing two quantities. But If we define angular momentum as one of our dimensions, then $\hbar$ can be a unit, right? I mean, surely it just depends on how we define things.

 

[Dale]

In Planck units the value of $\hbar$ is 1. So $\hbar$ could be considered the unit of action in Planck units. However, since the same symbol is used elsewhere for the quantity, I would not call it a unit since it would lead to confusion. I would call the unit the Planck action and say that 1 Planck action = $\hbar$.

 

[BruceW]

well, in Planck units, angular momentum is dimensionless. So it doesn't need units, right?

 

[Dale]

I don't think so. I think that in Planck units angular momentum has units of (Planck mass)(Planck length)²/(Planck time).

I.e. in Planck units I think that the dimensionful constants of nature are still considered dimensionful, it is just their values which are set to 1. I think that geometrized units consider the constants of nature to be dimensionless.

 

[BruceW]

yeah, that maybe right. I am not 100% sure on this stuff. I know that people will write stuff like "The rest mass of the electron is $0.51 \ \mathrm{MeV}$ ." So in this case, they are using Planck units where speed is dimensionless.

 

[Imabuleva]

The unit is part of the number, Bobie. When we say 0.51 MeV or 5 J*s, what we mean is multiply Joule times second times 5 or 0.51 times Mega-electron-volt. 0.51 means nothing without multiplying it by Mega-electron-volt.

 

[Imabuleva]

well, in Planck units, angular momentum is dimensionless. So it doesn't need units, right?

In Planck units, we define hbar to be 1. In this case, hbar still has units of angular momentum, but we're now working in angular momentum space.

 

[dauto]

You can, if you want, define h as a unit. What you cannot do - and that's the problem with bobie's logic - is to say that h = J*s. He repeated that claim many times.

 

[dauto]

Sorry, if I misunderstood, but I thought that h=J.s? wiki:
h = 1.054571726(47)×10−34 J·s
. Can two different units have same dimensions?

You cannot simply drop the 1.054571726(47)×10−34 factor out of the equation and expect it to still be correct.

Yes different QUANTITIES may happen to have the same dimension. Compare the unit for energy with the unit for torque.

 

[BruceW]

I think what bobie meant was that h has the same dimension as J.s (although maybe he did not explain what he meant very clearly). I don't think he was actually saying that it is possible to just drop the 1.05 X 10^-34

 

[BruceW]

In Planck units, we define hbar to be 1. In this case, hbar still has units of angular momentum, but we're now working in angular momentum space.

If we're using proper terminology, that should really be "hbar still has the same dimensions as angular momentum". I'm not sure what you mean that we are working in angular momentum space. Do you mean angular momentum is also dimensionless, if we define hbar to be dimensionless? I would agree on that.

 

[dauto]

I think what bobie meant was that h has the same dimension as J.s (although maybe he did not explain what he meant very clearly). I don't think he was actually saying that it is possible to just drop the 1.05 X 10^-34

Well, that's possible, but that's then a very sloppy way to express that and it's not surprising he got all the push back that he did. I would tell him what I tell my students " The symbol = means one thing and one thing only" It can only be used to express the mathematical identity between the left side and the right side of the equation.

 

[BruceW]

very true. I also don't like it when people write multiple equalities like $expression1=expression2=expression3=expression4...$ When they are trying to derive something. Even though this is correct, it makes it more difficult to see the reason for the logical steps. It's much better for there to be a short sentence giving a reason for each equality, instead of just writing down a string of equalities. (sorry for going off on a tangent).

 

[Imabuleva]

If we're using proper terminology, that should really be "hbar still has the same dimensions as angular momentum". I'm not sure what you mean that we are working in angular momentum space. Do you mean angular momentum is also dimensionless, if we define hbar to be dimensionless? I would agree on that.

Yes, that should say, "hbar still has the same dimension as angular momentum." By angular momentum space, I mean that our quantities will be divided by a factor of h. If the energy of a photon was once h*f, it will now just be 2*pi*f. So energy has dimension of inverse time, whereas it usually has the dimension of mass*length squared / time squared.

 

[BruceW]

ah right, I understand you now :)

 

[bobie]

I think what bobie meant was that h has the same dimension as J.s (although maybe he did not explain what he meant very clearly). I don't think he was actually saying that it is possible to just drop the 1.05 X 10^-34

I was not dropping nor thinking of dimensions, I have explained that I was just moving s from the right to the left side and did not know it is forbidden.
I did not see the necessity of dimensions and you confirmed they are not indispensable.

I do not know if I made it clear that the reason is that for a beginner 1.6*10^-19 J desn't mean much, whereas 2.4 *10¹⁴ Hz, B (or the infamous) h/s gives a clear, immediate picture of the real energy of a photon , in the region of visible light etc.
I was deceived by the fact that many times I have seen even mass converted to Hz , here:
http://en.wikipedia.org/wiki/Kilogram, under the picture "unit conversions" a Kg is converted to Hz
I am also muddled by the fact that two different entities can have same dimensions.

I want to express my sincere gratitude to all of you who have contributed to make this textbook thread about Planck constant.

Can you tell me if this concept of action is found anywhere else in physics, or is just an ad hoc creation for this particular instance?

 

[BruceW]

I was not dropping nor thinking of dimensions, I have explained that I was just moving s from the right to the left side and did not know it is forbidden.
I did not see the necessity of dimensions and you confirmed they are not indispensable.

it's not forbidden as far as I know. But it seems that people like to keep 'units' as a separate concept from 'quantities', although I don't see any fundamental difference.

I was deceived by the fact that many times I have seen even mass converted to Hz , here:
http://en.wikipedia.org/wiki/Kilogram, under the picture "unit conversions" a Kg is converted to Hz

In this case, they are also redefining dimensions, not just converting between units. I think it is sometimes called 'nondimensionalization'. This is the same thing as the electron's rest mass being given the dimensions of energy, and time being given the dimension of inverse energy, which is common among the particle physicists (I think). I mean, I think they like to write everything as having dimensions of energy to some power.

I am also muddled by the fact that two different entities can have same dimensions.

what is confusing, specifically? Or is it just surprising that angular momentum has the same dimensions as energy x time ?

 

[f95toli]

I was deceived by the fact that many times I have seen even mass converted to Hz , here:
http://en.wikipedia.org/wiki/Kilogram, under the picture "unit conversions" a Kg is converted to Hz

They did not "convert" mass to Hz, if you read the note it says that this is the frequency of a photon with the same energy (via the famouse E=mc^2 relation) as 1 kg of mass.

Expressing mass as energy or even temperature as is very common, and is often very convenient; even though it is NOT something one should do without keeping in mind what it is you are really doing.
You can for example if you want you can express nearly everything as temperature, since Boltzmann's constant kB allow you to go from energy to temperature. Hence, if you want you could express mass in Kelvin, but it wouldn't be very useful.
This to some extent "cultural" and depends on the field, particle physicists express nearly everything in energy (electron Volts), people in low temperature physics like Kelvin, in my area we tend to use Hz etc.
But again, none of these are "proper" conversions, they are just used because it simplifies some calculations since you don't need to keep track of some constant and/or it makes the numbers more managable.

 

[BruceW]

I guess you need to keep in mind exactly what you did to obtain the 'natural' equations. i.e. $c=1$ to get the natural equation $E^2=p^2+m^2$. Since if you forget the choice you made and forget the original equation, then you can't get back the original equation.