Planck's quantum theory

Introduction to Planck's Quantum in Chemistry:

At the end of the 19th century, scientists were curious about Black body radiation, a black body radiation means an idealized material that absorbs almost all types of electromagnetic radiation. No clues were identified with classical physics principles, how did this black body emit energy? According to classical physics, the emitted energy should increase with the increase in the frequency, this phenomenon is known as ultraviolet catastrophe, and the actual experimental results were contradictory. In 1900, German physicist Max Planck proposed the revolutionary theory, which today we study as Planck's Quantum theory. This theory gave the groundwork for Quantum physics. According to Planck's hypotheses, the energy emitted or absorbed by the body (e.g., Black body radiation) is in discrete or specific values, not random arbitrary values. He called it quantized values. From here comes another in quantum mechanics.

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This Story also Contains

1. Introduction to Planck's Quantum in Chemistry:
2. Quantization of Energy - Why Energy Comes in Bits?
3. Conclusion

In this article, we will cover the concept of Planck's quantum theory. This concept falls under the broader category of Atomic structure, which is a crucial chapter in Class 11 chemistry. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE, and more.

Quantization of Energy - Why Energy Comes in Bits?

When the energy is emitted and absorbed in discrete quantities, these discrete quantities are called Quanta, which is the quantization of energy. This term was later termed photons by Albert Einstein.

In short, we can say that atoms and molecules could emit (or absorb) energy only in discrete quantities known as quanta and not continuously. The following are certain phenomena that could not be explained by the wave nature of electromagnetic radiation and are explained by the particle nature:

Line spectra of atoms with special reference to hydrogen.

Max Planck suggested that the energy that is emitted or absorbed by the black body is not continuous but discontinuous in the form of small discrete packets of energy. Each such packet of energy is called a ‘quantum’. In the case of light, the quantum of energy is called a ‘photon’. The energy of radiation is proportional to its frequency ((ν)) and is expressed by the following equation:

E=hν=hcλ

where h is the Planck's constant, and it has a value equal to 6.63 10^-34 J-s

Let's try to solve the question based on the above formula,

Recommended topic video on ( Plank Quantum Theory)

Example 1: The nature of emission of radiation from hot bodies (black-body radiation).

Which one of the following is not characteristic of Planck's quantum theory of radiation

1) The energy is not absorbed or emitted in whole numbers or multiple quantums.

2)Radiations are associated with energy.

3) Radiation energy is not emitted or absorbed continuously but in the form of small packets called quanta.

4) This magnitude of energy associated with a quantum is proportional to the frequency.

Solution:

According to Plank's Quantum Theory,

Energy is absorbed or emitted not in a continuous manner, but in the form of small packets called Quanta.

The energy associated with the quanta is proportional to the frequency.

Hence, the answer is the option (1).

1. Ejection of electrons from a metal surface when radiation strikes it (photoelectric effect).

2. Variation of heat capacity of solids as a function of temperature.

Example 2: Which of the following statements is false?

1) Photon has momentum as well as wavelength.

2) The splitting of spectral lines in an electrical field is called the Stark effect.

3) The Rydberg constant has a unit of energy

4) (correct) The frequency of emitted radiation from a black body goes from a lower wavelength to a higher wavelength as the temperature increases.

Solution

As we learned in

The energy (E) of a quantum of radiation -

E=hv

Where h is plank's constant and ν is the frequency

When the temperature is increased, the black body emits high-energy radiation, from a higher wavelength to a lower wavelength.

Hence, the answer is an option (4).

Example 3:The energy of one quantum of light with a wavelength of 6500 A^o (1 A^o = 10^-10m) is

1) 5 x 10^-18J

2) (correct) 3.06 x 10^-19J

3) 8.02 x 10^-20J

4)9.0 x 10^-24J

Solution

As we learn

Planck’s Quantum Theory -

Atoms and molecules could emit (or absorb) energy only in discrete quantities known as quanta, and not continuously.

The energy of one quantum of light

E=hcλ=6.62×10−34×3×1086.5×10−7=3.06×10−19 J

Hence, the answer is the option (2).

Example 4: According to Planck's quantum theory, the energy of a quantum of radiation is given by:

1) E=hv
2) E=hcλ
3) E=hc2λ
4) E=hλ

According to Planck's quantum theory, the energy of a quantum of radiation is directly proportional to its frequency. This is given by the equation E=hv, where E is the energy of the quantum, h is Planck's constant (6.626×10−34 J s), and v is the frequency of the radiation.

Hence, the answer is the option (1).

Example 5: What is the wavelength of a photon with energy 3.0×10−19 J, according to Planck's quantum theory?
1) 1.15×10−7 m
2) (correct) 2.50×10−7 m
3) 5.56×10−7 m
4) 9.23×10−7 m

Solution

According to Planck's quantum theory, the energy of a photon is given by the equation E=hcλ, Where E is the energy of the photon, h is Planck's con (6.626×10−34 Js),cis thed the speed of light (3.0×108 m/s)(3.0×108 m/s)λ is the wavelength of the photon.

Rearranging this equation gives
λ=hcE

Plugging in the given values, we get
λ=(6.626×10−34 J s)(3.0×108 m/s)3.0×10−19 J≈2.50×10−7 m

Hence, the answer is the option (2).

Conclusion

We can conclude that Planck's quantum theory gave a whole new perspective and also a whole new paradigm shift in science, and we understood energy absorption and emission. The black body radiation which was initially not cleared by classical physics is much clearer in Quantum mechanics. Planck's postulate or Planck's Hypothesis explains the energy emitted and absorbed are in discrete quantities and termed as Quantization of energy and the term quanta termed Photons by Albert Einstein. The nature of emission or absorption of radiation from hot bodies (black-body radiation). The ejection of electrons from a metal surface when radiation strikes it called the photoelectric effect. Line spectra of atoms with special reference to hydrogen(Bohr's model of hydrogen).