Planck's Assumption

Max Planck's assumption that energy is not continuous, but rather comes in discrete packets, or quanta, is one of the most important and revolutionary ideas in physics. This was a radical departure from the prevailing view at the time, which held that energy was continuous.

Planck's assumption was based on his work on blackbody radiation, which is the radiation emitted by a perfect absorber of radiation. Planck found that the experimental data for blackbody radiation could only be explained if energy was quantized.

The quantum hypothesis, as Planck called it, led to the development of quantum mechanics, one of the most important and successful theories in physics. Quantum mechanics has revolutionized our understanding of the physical world, and it has led to the development of many new technologies, such as lasers and transistors.

Background:

In the early 1900s, physicists were studying the emission of light by hot objects. They found that the spectrum of light emitted by a hot object depends on the temperature of the object. For example, a red-hot object emits a continuous spectrum of light, while a white-hot object emits a spectrum with a peak in the blue region of the visible spectrum.

The reason for this is that the energy of light is quantized. This means that energy can only be emitted or absorbed in discrete packets, or quanta. The energy of each quantum is proportional to its frequency, which is related to the color of the light.

Red-hot object

A red-hot object is an object that is heated to a temperature at which it emits visible light in the red part of the spectrum. The color of an object is determined by the wavelength of light that it emits. Red light has a wavelength of about 700 nanometers. As an object is heated more and more, it emits light of shorter and shorter wavelengths. When an object is heated to a white-hot temperature, it emits visible light of all wavelengths, which is why it appears white.

The exact temperature at which an object becomes red-hot or white-hot depends on the material of the object and the way in which it is heated. For example, iron becomes red-hot at a temperature of about 800 degrees Celsius, while tungsten becomes red-hot at a temperature of about 1,500 degrees Celsius.

A red-hot object emits a continuous spectrum of light because the atoms in the object are emitting photons at a wide range of frequencies. This is because the atoms in the object are in a variety of energy levels, and they can emit photons with a wide range of energies. The energy of each photon is proportional to its frequency, so the photons emitted by a red-hot object have a wide range of frequencies.

White-hot object

A white-hot object is an object that is heated to a temperature at which it emits visible light of all wavelengths. This means that the object appears white, as it is reflecting all of the visible light that hits it. The exact temperature at which an object becomes white-hot depends on the material of the object and the way in which it is heated. For example, iron becomes white-hot at a temperature of about 1,538 degrees Celsius, while tungsten becomes white-hot at a temperature of about 3,370 degrees Celsius.

A white-hot object, on the other hand, emits a spectrum with a peak in the blue region of the visible spectrum because the average frequency of the photons emitted by the atoms in the object is higher. This is because the atoms in a white-hot object are more energetic than the atoms in a red-hot object. More energetic atoms can emit photons with higher frequencies, so the photons emitted by a white-hot object have a higher average frequency than the photons emitted by a red-hot object.

The quantization of energy explains why hot objects emit a continuous spectrum of light. When a hot object emits a photon, it can only emit a photon with a frequency that corresponds to one of the allowed energy levels of the object. This means that the object can emit photons at a wide range of frequencies, which gives rise to the continuous spectrum of light.

The peak of the spectrum of blackbody radiation shifts to higher frequencies as the temperature of the object increases. This is because the higher the temperature of the object, the higher the energy levels of the object. This means that the object can emit photons with higher frequencies, which shifts the peak of the spectrum to higher frequencies.

The study of the emission of light by hot objects led to the development of quantum mechanics, one of the most important and successful theories in physics. Quantum mechanics has revolutionized our understanding of the physical world, and it has led to the development of many new technologies, such as lasers and transistors.

• Planck's hypothesis: Planck hypothesized that the energy of light could only be emitted or absorbed in discrete packets, or quanta. He called these quanta "elementary units of action".
• Formula: Planck used his hypothesis to derive a formula to calculate energy of photons

E = nhf

Where, E is the energy of photon, n is the number of photons, h is the Planck's constant, and f is the frequency of photon.

Conclusion

Planck's assumption was a radical departure from the prevailing view at the time, which held that energy was continuous. However, it was a necessary step in the development of quantum mechanics, one of the most important and successful theories in physics.