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Planck’s Quantum Theory: By the end of the 20th century, Max Planck had put forward his theory of the quantized nature of electromagnetic waves. The smallest amount of energy that can be released or absorbed by electromagnetic radiation is known as quantum. Moreover, the amount of radiation absorbed or emitted is directly proportional to the amount of radiation.
Thus, the energy of radiation can be expressed as,
E = h v
In which, ‘E’ means the energy of the radiation,
‘h’ means Planck’s constant (6.626×10-34 J.s),
‘v’ means the frequency of the radiation
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Key Takeaways- Planck’s Quantum Theory, Electromagnetic Radiation, Black Body Radiation
Introduction to Planck’s Quantum Theory
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During the 20th century, Albert Einstein and Max Planck together constituted the fundamental theories of physics. He knew that radiation entropy had to be mathematically dependent on its strength in a high-frequency region if Wien law was held there. He also saw what this reliance should have on a low-frequency region to produce test results there.
Planck therefore thought that he should try to combine the two terms in a very simple way and turn the result into a formula related to radiation in its range.Therefore, he discovered ‘Planck Radiation Law.’
In addition, Planck had to consider that the oscillators that connect a black body and re-emit the phenomenon of attractive energy over them could not absorb this energy continuously but at different rates, in a quantum of energy; by statistically distributing these quanta, each contains an amount of energy equal to its quantity, on top of all the oscillators available to the black
Planck found the formula he had struck two months earlier. He added further proof of the value of his formula by using it to test the constant h (his value was 6.55 × 10-27 erg-second, close to the modern value of 6.626 × 10-27 erg-second). Therefore, he derived the formula to calculate the energy of the radiation.
It can be said that Planck’s mere assumption of quantization has been regarded as the birth of quantum theory in today's world. This view has renewed our understanding of atomic and subatomic processes.
Electromagnetic Radiation
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Electromagnetic ray is a type of energy that can be dispersed in a vacuum or by a medium material and has shown that the waves are particle-like as structures. Radio waves, microwaves, infrared, visible light, UV-rays, X-rays, gamma rays are electric rays. Electrical radiation or electric waves are created as a result of periodic changes in the electric field or magnetism. Depending on the frequency of these changes and the energy produced, different wavelengths of the electromagnetic spectrum are generated. All-electric waves propagate at the speed of light in space.
For understanding the concept of electromagnetic radiation, refer to this video
Therefore, to be precisely clear, the study of electromagnetism is about how electrical particles come together and have strong magnetic fields.
Read More: Boyle's law
Black body Radiation
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For the emission, a lower frequency is called the threshold frequency. Suppose the light is falling, it has a force equal to ‘hv.’ Besides the h, the value of ‘h’ is used as a binding force and the rest is given to the electron as kinetic energy. Therefore, the observation noted as follows:
- If the frequency is greater than the frequency limit: instead of emission and kinetic energy is given to extract electrons.
- If the frequency is equal to the size of the threshold, only emissions occur.
- If the frequency is less than the threshold, no discharge occurs and no kinetic energy is supplied.
The black body is a systematic object that can absorb all the electrical rays it encounters. After this, it begins to emit hot rays at a continuous rate depending on its temperature. The radiation emitted by a black body is called the radiation of a black body. The stars almost act like a black body.
The amount of radiation emitted by the length of each wavelength depends only on the temperature of the object and not on any other material, such as its chemical composition. This was explained statistically by German philosopher Max Planck in 1900. Scientists often refer to this as radiation. Alternatively, they use the term 'black body' radiation - a black body is an imaginary device that completely absorbs all the light it receives and shows nothing. The black body is also a perfect light bulb over all wavelengths, but there is a single wavelength where radiation is very strong.
Thermal substances emit more radiation than cold substances in all wavelengths. In addition, the object is very hot, short of the maximum length of its maximum discharge (see Figure 3). Keeping in mind that shorter wavelengths are associated with higher energy, this means that thermal objects emit far more energy radiation than cold objects - as the sensor might indicate.
Things to Remember
- Planck’s quantum theory considers energy radiation to be quantised in packets or bundles. The smallest such bundle is known as a quantum.
- Max Planck was the first to derive a relation for calculating the energy of a quantised electron. According to that formula, E = hγ
- The black body is a systematic object that can absorb all the electrical rays it encounters.
Read More: Thermodynamics
Sample Questions
Q1. Calculate the energy of a mole of photons of radiation whose frequency is 5 x 1014 Hz? (NCERT Question) (5 marks)
Ans: 100-watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emitted per second by the bulb.
Thus, the main postulates of Planck’s Quantum Theory are -
The object emits energy or absorbs energy at different values without interruption in the form of small packets or bundles.
A very small lump or power pack is known as a quantum. In the case of light, the light bulb is known as a photon.
Quantum energy absorbed or excreted is directly proportional to the amount of radiation.
The body or object can extract energy or absorb energy with a whole number of quantum multipliers such as ‘nhv.’ When ‘n’ is a whole number. Therefore, power can be entered or released such as hv, 2hv, 3hv, 4hv …… etc. not in the form of 1.5hv, 2.5hv… etc.
Thus, quantum theory can be applied in the quantum mechanics field, which includes quantum cryptography, quantum computing, the medical field, electrical appliances, lasers, etc.
Q2. It is given that the wavelengths of 2 electrons are 2000 A and 4000 A. Calculate the ratio of their energy. (3 marks)
Answer: As explained by the planck’s quantum theory,
E = hc/\(\lambda\)
E ∝ 1/\(\lambda\)
Hence, the ratio of the energy will be opposite to the wavelength.
E1/E2 = \(\lambda\)2/ \(\lambda\)1
So, ratio of energies = 4000/2000 = 2
Q3. Choose the incorrect statement: (2 marks)
1.The energy is not absorbed or emitted in whole number or multiples of quantum
2.Radiation is associated with energy
3.Radiation energy is not emitted or absorbed continuously but in the form of small packets called quanta
4.Magnitude of energy associated with a quantum is proportional to the frequency
Answer: The answer is option (1), since the energy is absorbed or emitted in whole number or multiples of quantum according to the quantum theory, as opposed to the statement given in option (1)
Q4. Calculate the energy that corresponds to a wavelength of 45 nm. (2 marks)
Answer: From the Max Planck Equation,
E = hc/\(\lambda\)
= 6.63 x 10-34 x 3 x 108 / 45 x 10-9 J
= 4.42 x 10-18 J
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