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2. Brief synopsis
In 1900, Max Planck explained the particle nature of light with his theory known as Planck's
quantum theory.
Planck proposed that light consists of discrete packets of energy called quantum. It solved the
mysteries of black body emissions in the ultraviolet region.
Planck’s quantum theory proposed the quantum nature of electromagnetic radiant
energies. It explained the interaction of light as a particle with the matter.
It proves the particle character of light with the phenomena such as the photoelectric effect
and black body radiations.
The equations of Maxwell and the study of electromagnetic radiations by Hertz successfully
proved the wave character of light with the phenomena such as diffraction and interference.
It is the basic theory of quantum mechanics. And it paved the way for the dual character of
matter.
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3. Postulates
A body can absorb and emit discontinuously tiny
packets of energy. Each small energy packet is
known as a quantum. Uniquely the term photon
denotes light energy.
These are the main postulates of Planck quantum theory:
Energy associated with quantum varies directly with the
frequency of electromagnetic radiation.
𝐄 = nhν
Where,
E= Energy of quantum
h= Planck constant
ν= frequency of electromagnetic radiation
n= non-zero positive integer
E = hν (For single photon)
(For ‘n’ number of photons)
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4. A body can accept or release whole number multiples of quantum.
For example- an object can give or take 1hν, 2hν, or 3hν, nhν units of energy.
Energy in fractions of a quantum can neither emitted nor absorbed.
For example- an object cannot transmit 1/2hν, 3/2hν, or 5/4hν units of energy.
The Planck-quantum law describes the relationship between the magnitude of photons and the
frequency of light.
Planck-quantum law
Planck quantum-frequency relationship:
To measure the frequency of a photon, we can use this formula.
It states that the magnitude of energy of a photon varies directly with its frequency.
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5. So, low-frequency radiations contain low energy. Conversely, high energetic radiations possess
high frequencies.
E = hν
Where,
E= Magnitude of energy of the photon. Its unit is joule in the SI system. And erg in the CGS
system.
h= Planck constant. And its value is 6.626 x 10-34 Joule second
ν= Frequency of light. And its unit is Hertz in both the SI and CGS systems. Hertz is equal to
second-1
Planck quantum-wavelength relationship:
It shows that the energy of a photon varies inversely with the wavelength of the light radiation.
E =
hc
λ
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6. Where,
E= magnitude of energy of photon
h= Planck constant. And its value is 6.626 x 10-34 joule second
c= velocity of light in vacuum. And its value is 3x108 m/sec in the SI system
λ = wavelength of light
By substituting the values of the Planck constant and the velocity of light in the above equation, we
get;
E =
(6.626 × 10−34
Js) × (3 × 108
m/sec)
λ
E =
19.878 × 10−26 joules
λ
With this equation, we can calculate the energy of light radiation from its wavelength data.
Planck quantum-wavenumber relationship:
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7. It states that the wavenumber of the light radiations varies directly with its photon energy.
E = hcῩ
Where,
E= magnitude of light energy
h= Planck’s constant
Ῡ= Wavenumber of the photon
c= Velocity of light in vacuum
By substituting h and c values, we get;
𝐸 = (6.626 × 10−34 𝐽𝑠) × (3 × 108 𝑚/𝑠𝑒𝑐) × Ῡ
E = 19.898 × 10−26 × Ῡ joules
To conclude, Planck's quantum theory helps calculate the photon energies from the known
data of wavelength, frequency, or wavenumber of electromagnetic radiation.
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8. Overview of Planck quantum theory
Planck's quantum theory explains the quantum mechanical phenomenon of thermal
electromagnetic radiations emitted by black bodies.
It determines the spectral density of black body radiations at a constant temperature when
there is no net flow of matter or energy between the black body and its surrounding.
Planck discovered the term "quantum" to denote the minimum amount of energy emitted or
absorbed by the oscillator.
The amount of energy less than a quantum is neither emitted nor absorbed
The incremental energy changes of the black body emissions showed their spectral intensity
from low frequency to higher frequency radiations.
Hence, at thermal equilibrium the radiation released from the cavity of the black body
experimentally agreed with the quantum assumptions of Max Planck.
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9. Applications of Planck quantum theory
Planck's quantum theory is the fundamental theory of quantum mechanics. It has the following
applications:
1. The semiconductor-based electronic gadgets follow the quantum nature of matter.
2. Fiber optic telecommunications and laser devices involve the phenomenon of photon
interaction with matter.
3. Atomic clocks fitted in satellites for GPS navigation follow quantum physics.
4. MRI (Magnetic resonance imaging) scan works on the quantum nature of light and matter.
Limitations of Planck quantum theory
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10. It described the energy emissions of periodic systems. It does not apply to non-periodic objects.
It is silent about the relative intensities of spectral lines.
It proposed the electron as a spin-less oscillating object. And it did not explain the spin motion of
the electron.
Planck constant
Planck constant is a fundamental physical quantity. It explains the particle nature of light on the
atomic and sub-atomic levels. Thus, Planck's constant plays a vital role in quantum theory.
It is a number that helps to calculate the energy of light. The value of Planck's constant
is 6.626 X 10-34 joule second in the SI system.
The symbol "h" denotes it.
Planck's constant is equal to the ratio of the light energy to its frequency.
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11. h =
E
ν
Where,
h= Planck constant
E= energy of light
ν= frequency of photon
When Planck researched black body emissions in 1900, he found that a proportionality constant is
essential in his empirical formula to match the experimental results. With effort, he calculated the
value of Planck's constant to measure the quantum energy.
Value of Planck constant
The value of Planck's constant is 6.626 X 10-34 joule second in the SI system.
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12. In the CGS system, the value of Planck’s constant is 6.626 x 10-27 erg second
In the atomic units, h value is 4.136 x 10-15 eV second
Value of h
SI system
6.626 x 10-34 joule second
6.626 x 10-27 erg second 4.136 x 10-15 eV second
1 joule =107 erg 1 eV = 1.602 x 10-19 joule
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13. Experiments used to determine Planck’s constant:
The following are a few experimental methods to compute Planck's constant practically
1. From Faraday's constant in electrolysis experiments
2. Particle accelerator method
3. Kibble balance
We use LED (light emitting diodes) to determine Planck's constant experimentally. It is due to its
ability to emit different colored radiations at different threshold voltages while producing
electrons.
Applications of Planck constant
1. To calculate the energy of an electron in the nth orbit
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14. Bohr's atom consists of discrete stationary orbits at fixed distances from the central core.
The energy of an electron in the nth orbit is En.
En = −
hcR∞
n2
2. In de-Broglie wavelength
Louis de-Broglie suggested that Planck's constant expresses the proportionality relationship of
momentum and quantum wavelength in particles.
λ =
h
p
Where,
p = momentum of the particle
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15. 3. In Photoelectric effect
• Isaac Newton explained the photoelectric effect by considering the quantum theory of
Max Planck.
• The frequency of incident light is the sole factor that decides the kinetic energy of the
photoelectron emitted from the metal surface. And this is independent of the light
intensity.
• If the frequency of incident light is higher than the material's work function, a rise in light
intensity increases the photoelectron emissions.
• Planck-Einstein relation determines the size of the energy bundle. It is named a photon
later.
E = hf
Where,
E = kinetic energy of photo electron
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