[hamdani yusuf]

None of which changes the dimensions of h or ħ : joule.second. 2π is a dimensionless constant.

Radian is indeed a dimensionless unit.
When you have the light frequency in radian/second unit instead of Hertz, you can multiply it with ħ instead of h to get the energy.
https://en.wikipedia.org/wiki/Radian

The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit

[alancalverd]

radian/sec is not a frequency but a rate of change of angle or heading. A "standard rate 1 turn" in an airplane is 0.0524 radian/second.

[hamdani yusuf]

radian/sec is not a frequency but a rate of change of angle or heading. A "standard rate 1 turn" in an airplane is 0.0524 radian/second.

Perhaps you should stick to commonly used definition of any concepts, unless you have a strong reason not to do so.

The radian per second (symbol: rad⋅s−1 or rad/s) is the unit of angular velocity in the International System of Units (SI). The radian per second is also the SI unit of angular frequency (symbol ω, omega). The radian per second is defined as the angular frequency that results in the angular displacement increasing by one radian every second.
https://en.wikipedia.org/wiki/Radian_per_second

[hamdani yusuf]

h/2π = ħ is still joule.sec but 2π turns up in so many calculations that it is simply a more compact way of writing equations.

What do you think is the unit of ħ?
What's its value?

[alancalverd]

Nothing to do with what I think. It is defined as   

h = 6.62607015?10−34 J⋅Hz−1, so ħ = 1.054571817...?10−34 J⋅s or thereabouts.

I can't apologise for the irrationality of π.

[hamdani yusuf]

An antenna is oscillating at 1 billion radian per second. What's the energy of its photon?

[Origin]

An antenna is oscillating at 1 billion radian per second. What's the energy of its photon?

Seriously?  What do you think the energy of a photon is from an antenna oscillating at 57.3 billion degrees per second?  Does the question even make sense to you?

[hamdani yusuf]

An antenna is oscillating at 1 billion radian per second. What's the energy of its photon?

Seriously?  What do you think the energy of a photon is from an antenna oscillating at 57.3 billion degrees per second?  Does the question even make sense to you?

If it wasn't obvious to you yet, I referred to the electric field in the antenna.

[alancalverd]

The question doesn't make sense. 10⁹ rad/sec is a rate of rotation, so presumably we are looking at a betatron, not an antenna. The electron energy, and hence the energy of any photons emitted, depends on the radius of the torus.

I may have time to do the calculation later, but the dog needs a walk!

[Bored chemist]

109 rad/sec is a rate of rotation,

Not necessarily.
https://en.wikipedia.org/wiki/Angular_frequency
In which case the answer isn't hard to calculate.
But I don't see any point.
Certainly not any point that justifies the thread necromancy.

[alancalverd]

The unit hertz (Hz) is dimensionally equivalent, but by convention it is only used for frequency f, never for angular frequency ω. This convention is used to help avoid the confusion that arises when dealing with quantities such as frequency and angular quantities because the units of measure (such as cycle or radian) are considered to be one and hence may be omitted when expressing quantities in SI units.

So why make life difficult by ignoring a convention?

Anyway I get 10^-7 eV

[hamdani yusuf]

The question doesn't make sense. 10⁹ rad/sec is a rate of rotation, so presumably we are looking at a betatron, not an antenna. The electron energy, and hence the energy of any photons emitted, depends on the radius of the torus.

I may have time to do the calculation later, but the dog needs a walk!

Photonic interpretation for Planck's law states that hf is the energy of one photon. Thus radius of the
torus or antenna doesn't affect photon energy, as long as the frequency can be kept the same.

[hamdani yusuf]

An antenna is oscillating at 1 billion radian per second. What's the energy of its photon?

Seriously?  What do you think the energy of a photon is from an antenna oscillating at 57.3 billion degrees per second?  Does the question even make sense to you?

If it wasn't obvious to you yet, I referred to the electric field in the antenna.

For those who are not familiar with electronics in radio communications, I can give a more visually accessible example. A bar magnet is rotated with axis perpendicular to the magnetic field inside the magnet. The angular speed is 3000 rpm (rotation per minute) , which is typical for industrial motors. The question is the same, what is the photon energy radiated by the rotating magnet?

[alancalverd]

Photonic interpretation for Planck's law states that hf is the energy of one photon. Thus radius of the
torus or antenna doesn't affect photon energy, as long as the frequency can be kept the same.

But it does affect the energy of the electron that generates the photon. It all gets a bit complicated as it's quite easy to get an electron up to 0.9c in a betatron, at which point the relativistic corrections become very significant. 

[hamdani yusuf]

Photonic interpretation for Planck's law states that hf is the energy of one photon. Thus radius of the
torus or antenna doesn't affect photon energy, as long as the frequency can be kept the same.

But it does affect the energy of the electron that generates the photon. It all gets a bit complicated as it's quite easy to get an electron up to 0.9c in a betatron, at which point the relativistic corrections become very significant. 

It supposed to affect the number of photons radiated by the antenna.
How does relativistic corrections affect the photon frequency, and its energy?

[Bored chemist]

The question is the same, what is the photon energy radiated by the rotating magnet?

Small.
3000 RPM is 50Hz so the photon energy is 50 times Planck's constant.

That's high school maths. Why have you reopened a long-dead thread to ask about it?

[Bored chemist]

Photonic interpretation for Planck's law states that hf is the energy of one photon. Thus radius of the
torus or antenna doesn't affect photon energy, as long as the frequency can be kept the same.

But it does affect the energy of the electron that generates the photon. It all gets a bit complicated as it's quite easy to get an electron up to 0.9c in a betatron, at which point the relativistic corrections become very significant. 

Earth calling Alan.
He's not talking about a betatron.

On one hand, that's a pity because it's more interesting.
On the other hand, it may be just as well because I think he'd make a mess of it.

[alancalverd]

It supposed to affect the number of photons radiated by the antenna.

Nonsense. It affects the energy of the photons, not the number. More electrons -> more photons, electrons oscillating faster -> higher photon frequency and E = hf

How does relativistic corrections affect the photon frequency, and its energy?

You need to apply relativistic corrections to the electron velocity as you increase its kinetic energy. If energy E gives it a speed of 0.9c, 2E won't make it travel at 1.8c,

[alancalverd]

He's not talking about a betatron.

He's talking about the angular speed of an electron. What else would you call a device that makes electrons orbit at a constant 10⁹radians per second?

[Eternal Student]

Hi.

For the oscillating electron in the antennae:
I'm making  10⁹   radians/sec   --->   frequency of 159 MHz.    That's the top end of the radio frequencies, maybe early microwave.
Energy of a photon  ≈  1.05 x  10²⁵  Joules    =   6.6 x 10^-7  eV
and I think @alancalverd  suggested  10^-7   eV.

I think you can get electrons to oscillate in an ordinary metal antenna at about this rate.   If you go much faster you can start getting reflection of the electrons from the crystal lattice and stuff happens.   I'm not an engineer but I believe the antenna gets hot and you end up with a spread of frequencies released rather than a clear emission at one frequency.

@Bored chemist   seems to have done the rotating magnet and I agree with that answer.

A slightly more interesting question for the rotating magnet is as follows:
    In open space, this rotating magnet is emitting radiation and thus losing energy.    Where is that energy coming from?  If the rotating magnet reduces its (rotational) k.e.  - where is the torque coming from that makes that happen?

Best Wishes.