# Planck's equation and upper and lower bounds on the energy of a photon

• B
• PainterGuy
In summary: The exact point where this happens is still a topic of research. In summary, Planck's equation describes the relationship between energy and frequency for a photon, with no lower or upper bounds on the energy of the photon. However, at very high energies, other factors may come into play and the concept of a "photon" may no longer be applicable.
PainterGuy
Hi,

Planck's equation is written as E=hν where "E" is energy of a photon, "h" is Planck's constant having value 6.626 070 15 x 10-34 Js, and "ν", Greek letter nu, is frequency.

Violet color has frequency range between 790–666 THz (Tera =10^12). If a violet photon of frequency 7.5 x 10^14 Hz is considered, its energy is 5 x 10^-19 Joule.

Note that frequency and wavelength are inversely proportional, if frequency increases the wavelength decreases and vice versa.

To calculate the energy of 'n' photons of same frequency, the equation could be written as E=nhν.

In the equation above, 'n' is discrete, 'h' is a constant but 'ν' is a real number which means it can ideally take on any real value.

Question 1: Are there any lower or upper bounds on the energy of a photon? I don't think a photon could have energy of 0 J because it would mean frequency of 0 Hz and at the same time to have infinite energy the photon must have infinite energy.

Question 2: I've always thought of a photon as a tiny wiggly wavy packet. An EM wave with frequency 30 Hz has the corresponding wavelength of 10,000 km (longer than the radius of the Earth). Well, this is no longer tiny wiggly wavy packet. How do I visualize a photon in such a case?

1: https://en.wikipedia.org/wiki/Planck_constant
2: https://simple.wikipedia.org/wiki/Planck_constant
4: https://physics.stackexchange.com/q...the-highest-possible-frequency-for-an-em-wave

Klystron and Delta2
PainterGuy said:
Question 1: Are there any lower or upper bounds on the energy of a photon?

PainterGuy said:
Question 2: I've always thought of a photon as a tiny wiggly wavy packet. An EM wave with frequency 30 Hz has the corresponding wavelength of 10,000 km (longer than the radius of the Earth). Well, this is no longer tiny wiggly wavy packet. How do I visualize a photon in such a case?
Just skip the "tiny" bit.

PainterGuy
Photons are not "tiny little balls". One should never think about photons in terms of particles but in terms of electromagnetic fields. Then all apparent inconsistencies are overcome.

PainterGuy, Klystron and Lord Jestocost
PainterGuy said:
Question 2: I've always thought of a photon as a tiny wiggly wavy packet. An EM wave with frequency 30 Hz has the corresponding wavelength of 10,000 km (longer than the radius of the Earth). Well, this is no longer tiny wiggly wavy packet. How do I visualize a photon in such a case?

To yield a wave packet, one needs a superposition of traveling waves with an appropriate distribution of various frequencies.
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/wpack.html#c1

PainterGuy and vanhees71
As posts #2 and #3 answer your questions, this explanation of Extremely Low Frequency (ELF) technology may help visualize long wavelength electromagnetic fields.

The wikipedia article provides an ELF lower limit of 3hz but I understand research and technology has progressed to lower frequencies / longer wavelengths. From the article:

Difficulties of ELF communication

One of the difficulties posed when broadcasting in the ELF frequency range is antenna size, because the length of the antenna must be at least a substantial fraction of the length of the waves. Simply put, a 3 Hz (cycle per second) signal would have a wavelength equal to the distance EM waves travel through a given medium in one third of a second. When the refractive index of the medium is greater than one, ELF waves propagate slower than the speed of light in a vacuum. As used in military applications, the wavelength is 299,792 km (186,282 mi) per second divided by 50–85 Hz, which equals around 3,500 to 6,000 km (2,200 to 3,700 mi) long. This is comparable to the Earth's diameter of around 12,742 km (7,918 mi). Because of this huge size requirement, to transmit internationally using ELF frequencies, the Earth itself forms a significant part of the antenna, and extremely long leads are necessary into the ground.

PainterGuy
PainterGuy said:
I've always thought of a photon as a tiny wiggly wavy packet.
Here are some macroscopic analogies to quantum mechanical particles, which share some of their properties:

PainterGuy
A.T. said:
Here are some macroscopic analogies to quantum mechanical particles, which share some of their properties:

Thank you for sharing these interesting videos but I think these videos are based on pilot wave theory which isn't considered mainstream interpretation on quantum mechanics. These videos helps a lot with intuitive and basic understanding. Please correct me if I'm wrong. Thank you!

PainterGuy said:
These videos helps a lot with intuitive and basic understanding. Please correct me if I'm wrong.
Here are more, but I will leave the correcting to those with more expertise on quantum mechanics:

PainterGuy
PainterGuy said:
Are there any lower or upper bounds on the energy of a photon?

Mathematically speaking, no: Planck's formula can describe a photon of any finite energy greater than zero.

Physically speaking, most physicists believe that at high enough energies, a "photon" description would no longer be valid because other physics would come into play beyond simple quantum electrodynamics.

PainterGuy and vanhees71

## 1. What is Planck's equation?

Planck's equation, also known as the Planck-Einstein relation, is a fundamental equation in quantum mechanics that describes the relationship between the energy of a photon and its frequency. It states that the energy of a photon is equal to its frequency multiplied by a constant known as Planck's constant.

## 2. What are upper and lower bounds on the energy of a photon?

The upper and lower bounds on the energy of a photon refer to the minimum and maximum possible energy that a photon can have. The lower bound is known as the threshold energy, which is the minimum energy required for a photon to exist. The upper bound is the maximum energy that a photon can have, which is determined by the frequency of the photon.

## 3. How do upper and lower bounds on the energy of a photon relate to Planck's equation?

Planck's equation provides a mathematical relationship between the energy of a photon and its frequency. This means that the frequency of a photon determines its energy and therefore, the upper and lower bounds on its energy. The higher the frequency, the higher the energy and the closer the photon's energy is to the upper bound.

## 4. Can the energy of a photon exceed the upper bound?

No, the energy of a photon cannot exceed the upper bound determined by its frequency. This is because the energy of a photon is directly proportional to its frequency and Planck's equation dictates that the energy cannot be greater than the product of the frequency and Planck's constant.

## 5. How does Planck's equation impact our understanding of the behavior of light?

Planck's equation revolutionized our understanding of the behavior of light by introducing the concept of quantization, which states that energy can only exist in discrete units. This explains the observed behavior of light, such as the photoelectric effect, and has paved the way for further developments in quantum mechanics.

• Quantum Physics
Replies
78
Views
3K
• Quantum Physics
Replies
3
Views
1K
• High Energy, Nuclear, Particle Physics
Replies
1
Views
961
Replies
2
Views
851
• Introductory Physics Homework Help
Replies
48
Views
2K
• Quantum Physics
Replies
19
Views
6K
• High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
• Quantum Physics
Replies
3
Views
3K
• Optics
Replies
6
Views
5K
• Introductory Physics Homework Help
Replies
7
Views
1K