# The energy of a photon

Gold Member
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?

Staff Emeritus
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 is missing a unit of measure.

For some unit relationships, try

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

Gold Member
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?

Gold Member
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...?

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Gold Member
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?

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]

1 person
Gold Member
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?

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.

Gold Member
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?

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. ]

Mentor
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.

1 person
Gold Member
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)?

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

Gold Member
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?

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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! :grumpy:
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.

Gold Member
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?

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

Gold Member
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?

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Gold Member
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?

Gold Member
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?

Gold Member
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.

1 person
Gold Member
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.

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.

1 person
Gold Member
Thanks, that is very helpful indeed

Gold Member
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.

Gold Member
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?

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 here. You'll notice that nearly all of them have units.

Gold Member
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
ke: Coulomb's constant
me:the mass of the electron
mp:the mass of the proton
etc.
etc.

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

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Homework Helper
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.

Mentor
2021 Award
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##.

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

Mentor
2021 Award
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.