# The energy of a photon

Gold Member

## Main Question or Discussion Point

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?

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Drakkith
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.

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?

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

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?

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]

• 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?

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.

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?

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]

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  miles/hour x  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
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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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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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! :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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Bandersnatch
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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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?

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.

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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.