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?

Answers and Replies

Related Other Physics Topics News on Phys.org
Drakkith
Staff Emeritus
Science Advisor
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?

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

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...?

Last edited:
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
Science Advisor
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
Science Advisor
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
Science Advisor
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 [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
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)?

Last edited:
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?

Last edited:
Bandersnatch
Science Advisor
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?

Last edited:
Bandersnatch
Science Advisor
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?

Last edited:
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.

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.