Planck's constant explanation-Jayam chemistry learners
Planck's constant of quantum theory
Introduction to Planck's constant
It is a
fundamental physical quantity. Its magnitude and unit are independent of other
physical quantities for measurements.
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 symbol
"h" denotes it.
It is a
constant value that does not change with time. So, it is a universal constant.
The value
of Planck's constant is 6.626 X 10-34 Js in the SI system.
Today's blog post topic is Planck's constant explanation. It covers definitions, units, values, and applications of Planck's constant.
Table of contents:
Introduction to Planck’s constant
Who discovered Planck’s constant?
Experimental methods to determine Planck’s constant
Applications of Planck’s constant
Difference between the Planck’s constant and the reduced Planck’s constant
Multiple choice questions and answers of Planck’s constant
Frequently asked questions and answers of Planck’s constant
Our e-book:
To download a beautiful PPT notes of Planck's quantum theory, click the highlighted link.
What is Planck's constant?
It is a
constant physical quantity that relates the energy of a photon with its
frequency.
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| Fatafat checklist of Planck's constant |
According
to Planck's quantum theory, the magnitude of radiation energy varies directly with
its frequency.
E ∝ ν
Where,
E= energy of
light
ν= frequency of
light
For an
accurate result, Planck introduced a constant value in the mathematical formula
that is Planck's constant.
E = hν
Where, h=
Planck’s constant
Consequently, the
energy of a photon is equal to the product of Planck's constant and frequency
of light.
Therefore, all
the light radiations at constant frequency possess the same energy.
Planck's constant
is equal to the ratio of the light energy to its frequency.
h = E/ν
Additional reference:
What is the experimental method used to
determine Planck's constant?
Who discovered Planck's constant?
A German
theoretical physicist, Max Planck, introduced it.
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.
Max Planck
received the Nobel Prize in physics in 1918 for his work on the energy quanta.
Units of Planck's constant:
In the SI
system, the unit of Planck's constant is joule hertz-1 (or) joule
second.
h = E/ν
The unit of
energy in the SI system is the joule. And frequency unit is hertz.
h=joule/hertz
h=joule Hertz-1
One hertz
is one cycle per second.
Hertz=1/second
h=joule second
In case we express energy in electron volts, the unit of Planck's constant is eV hertz-1 or eV second.
In the CGS
system, the unit of Planck's constant is erg hertz-1 (or) erg
second.
Because the
unit of energy in the CGS system is the erg. And frequency unit is hertz.
Mind map of Planck's constant:
Planck's constant, the
name itself, signifies that it is a fixed numerical value invented by the
physicist Max Planck, the father of quantum mechanics. Planck quantum law
proposed the directly proportional variation of photon energy with the
radiation frequency. Planck's constant was the empirical fitting parameter in
the Planck quantum law for precise measurements of the magnitude of quantum.
It is a globally fixed
value independent of time and other experimental conditions. And its value is
equal to the proportion of quantum energy to the frequency of light. Hence, the
frequency data of spectral lines gives the size of the photon and vice versa.
Not only in spectral
evaluations, Planck's constant plays a vital role in the measurements of the
de-Broglie wavelength and photoelectric effect. Even though it is an unchanging
number, a few experimental methods measure Planck's constant value in real time.
They are the particle accelerator method and Kibble balance.
Click the link of
Planck's constant to view our mind map.
Value of Planck's constant:
In the SI
system, the value of Planck's constant is
In the CGS system, the value of Planck’s constant is 6.626
x 10-27 erg second
Explanation;
1 Joule = 107
erg
h = 6.626 x 10-34
joule second
h = 6.626 x 10-34
x 107 erg second
h = 6.626 x 10-27
erg second
In atomic units system, the value of Planck's constant is 4.136 x 10-15 eV second
Where electron volt is the unit of energy and the second is the unit of frequency in the atomic units system.
Here is the conversion of the Planck constant from the SI system to the atomic system of units.
Explanation;
h = 6.626 x 10-34 joule second1 eV = 1.602 x 10-19
joule
h = 6.626 x 10-34
/ 1.602 x 10-19
eV second
h = 4.136 x 10-15
eV second
Here is a table for
the value of Planck's constant in all three systems.
| Units of system | Planck constant value |
|---|---|
| SI system | 6.626x10-34 joule second |
| CGS system | 6.626x10-27 erg second |
| Atomic units | 4.136x10-15 eV second |
Here is a link to our
visually designed table on the value of Planck's constant.
Experimental methods used to determine Planck's constant
- From Faraday's constant in electrolysis experiments
- Particle accelerator method
- 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.
Why did Planck introduce h?
Classical
physics interpretations of black body emissions assumed a continuum spectrum at
thermal equilibrium.
But, it did
not match well with the experimental observations.
Planck
predictions of discrete energy packets for black body radiations described the
spectral distribution of thermal radiation at all temperatures.
His quantum
theory depicts energy variations in whole numbers multiples of quantum rather
than a random value.
Hence, the
black body or any object can have a set of definite periodic energy
installments.
This
specific energy value is determined by Planck's constant. So, he introduced
Planck's constant in the empirical relation.
Alternatively,
quantum energy is the integral multiple of the product of Planck's constant and
frequency of light radiation.
Consideration
of discrete energy increments for black body emissions proved the quantum
nature of electromagnetic radiations.
It laid the foundation for quantum mechanics.
Applications of Planck's constant:
1. To determine the wave characteristics of electromagnetic radiation:
By Planck's
quantum equation, we can compute the energy of a photon from the frequency of
light and vice versa.
Planck's
constant not only determines the frequency of radiation. Besides, it helps to
measure other wave characteristics of electromagnetic radiation.
We know the product of frequency and wavelength is equal to the velocity of the light in a vacuum.
c = λ x ν
It declares
the inversely proportional relationship between them. And this mathematical
relation helps to determine the wavelength of light from the known quantum
energy values.
E = hc/λ
Here is the
relationship between the wavelength and frequency of light.
By substituting
the constant values, we get;
E = (6.626 x 10-34)
x (3 x 108) /λ joules
E = 19.878 x 10-26
/λ joules
Similarly,
it assists in measuring the wavenumber of electromagnetic radiation from the
following mathematical formula.
E = hcῩ
By substituting the values of Planck's constant and velocity of light, we get;
E = {(19.878 x 10-26) x Ῡ} joules
2. It helps to determine other Planck units such as Planck's mass, Planck's length, etc.
3. Black body radiations
It regulates the average energy associated
with each quantum mode by the Planck distribution law.
4. 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= h.f
Where,
E= kinetic energy
of photo electron
f= frequency of
incident light
5. To calculate the energy of an electron in the nth orbit
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
6. To compute the 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.
λ = de-Broglie wavelength
Reduced Planck's constant:
- Dividing
Planck's constant by 2π gives reduced Planck's constant.
- The symbol
“ħ” (h-bar) denotes it.
- Its formula
is
- Implicit to Planck's constant is frequency measured in hertz.
- Hertz is the unit of frequency denoting one complete cycle per second.
- Mathematically,
one cycle completion implies 360 degrees (or) 2π radians.
- Thus, the reduced Planck's constant refers to the angular frequency in radians per second. But, Planck's constant represents linear frequency in hertz.
- Neil Bohr introduced the reduced Planck's constant to express quantized angular momentum of electron orbits.
- Angular momentum = mvr = nħ
- It has the same units as angular momentum.
- Kg m2 s-1 (or) joule second is its SI unit. Similarly, g cm2 s-1 (or) erg second is its CGS unit.
- The reduced
Planck's constant in the natural unit is 1. Because Planck's constant in
natural units is 2π.
- The reduced Planck's constant value in the SI system is approximately 1.054 X 10-34 joule second.
Difference between the Planck's constant and the reduced Planck's constant:
| Planck's constant | Reduced Planck's constant |
|---|---|
| It is the ratio of light energy to its frequency | It is the ratio of Planck's constant and 2π |
| It defines linear frequency in hertz | It defines angular frequency in radians per second |
| Max Planck introduced it to measure photon energy | Neil Bohr introduced it to express quantized angular momentum of electron orbits |
| In the SI unit, its value is 6.626 x 10-34 joule second | In the SI unit, its value is 1.054 x 10-34 joule second |
| Its natural unit is 2π | Its natural unit is 1 |
| The symbol "h" denotes it | The symbol "ħ" denotes it |
Here is our Pinterest
image that explains the difference between Planck's constant and reduced
Planck's constant.
Multiple choice questions and answers of Planck's constant
1. Planck constant is
a ______________
A. a number
B. a fixed
alpha-numeric value
C. time-dependent
constant
Answer:
A number
2. Planck constant
defines_____________
A. particle nature of
photon
B. size of a photon
C. Both A and B
Answer:
Both A and B
3. Electromagnetic
radiation having a 3 Hz frequency comprises 12 j energy. So, using E=hν, calculate the value of h.
A. 36 joule second
B. 6.626 x 10-34
joule second
C. 0.25 joule second
Answer:
6.626 x 10-34
joule second
4. What is
Einstein-Planck's law?
A. E=hν
B. E=hf
C. E=hcν
Answer:
E=hf
5. What is Planck
quantum formula?
A. E=hν
B. E=hf
C. E=hcν
Answer:
E=hν
6. What is the natural
unit of Planck's constant?
A. 1
B. 2π
C. infinite
Answer:
2π
7. Planck's constant
defines the proportionality relationship of____________
A. photon energy to
the radiation frequency
B. radiation frequency
to the photon energy
C. photon energy to
the speed of light in a vacuum
Answer:
Photon energy to the
radiation frequency
8. By Planck's quantum
theory, the quantum magnitude and radiation frequency vary___________________
A. directly
B. inversely
C. equal to h
Answer:
Directly
9. Quantum
means___________
A. Energy particle
B. Electromagnetic
wave
C. Charge of photon
Answer:
Energy particle
10. If the unit of
frequency is hertz, then what is the unit of Planck's constant in the CGS
system?
A. joule hertz
B. erg hertz-1
C. erg hertz
Answer:
Erg hertz-1
Frequently asked questions and answers on Planck's constant topic:
Planck's
constant indicates the quantization of light and matter on the atomic and
subatomic levels.
In the
atomic unit system, eV is the unit of energy. It partially depends on Planck's
constant to define the quantum nature of light.
The physical
meaning of h describes the basic features of the physical world.
So, eV
seconds is the unit of Planck constant in the atomic unit system.
Planck's
constant defines the photon energy based on the frequency of light.
The formula to measure the magnitude of photon is E = hν
The symbol
'h' denotes it.
It
describes the quantum nature of light by supporting Planck's discrete energy
emission assumptions.
It
expresses the size of a photon in Einstein-Planck's law.
E=hf (Einstein-Planck's law)
Where,
f= frequency of light radiation
When
electric current passes through LED, it emits photons in the visible region of
the electromagnetic spectrum.
The color
of the LED determines the energy associated with the photon.
LED emits
different colored radiations at different threshold voltages while producing
electrons.
Measuring
the threshold voltage at known emission wavelengths gives Planck's constant
value.
In 1900,
the German theoretical physicist discovered Planck's constant to express the
spectral radiance of the black body.
The SI unit of the Planck constant is joule
second, and the CGS unit is erg second.
The value of Planck constant is 6.626 X 10-34 joule second or 6.626 X 10-27 erg second.
Reference:
For more
information on Planck’s quantum theory topic, kindly refer our previous blog
articles.
(1)
Postulates of Planck’s quantum theory
(2) MCQ questions on Planck’s quantum theory