Planck's theory numerical problems- Jayam chemistry learners
Numerical problems on Planck quantum theory
Planck quantum theory outlines the particle nature of the energy of light. Max Planck, in the year 1900, narrated the blackbody emissions as the particles of radiant energy known as quantum. And his theory is widely renowned as Planck quantum theory. Today's blog post discusses numerical problems of Planck quantum theory and Planck constant topics.
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| Numerical problems of Planck quantum theory |
Postulates of Planck quantum theory
Numerical problems of Planck quantum theory
Definitions of the terms related to Planck quantum theory
PPT on MCQs of Planck quantum theory
Numerical problems of Planck’s constant
Postulates of Planck quantum theory
A body radiates integral bundles of energy known as quantum.
And in the case of light, the chunks of energy are named photons.
The magnitude of energy of radiations varies directly with
their frequencies.
E ∝ ν
The discrete energy transmissions take place in whole number
multiples of quantum.
Numerical problems of Planck quantum theory
Here is a PowerPoint presentation that discusses the numerical problems of Planck's quantum theory.
Note: (Scroll from 1 to 14 slides to unlock all numerical problems)
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Definitions of the terms related to Planck quantum theory
Let us discuss the terminology of Planck's quantum theory;
1. Light:
Light is electromagnetic radiation that a human eye can
perceive.
Its wavelength ranges between 380 nm to 700 nm. It occupies
the visible region of the electromagnetic spectrum.
For additional information on light, visit here.
2. Electromagnetic radiation:
In classical physics, electromagnetic radiation is a
propagating wave of combined electric and magnetic fields.
In modern quantum theory, electromagnetic radiation is the
flow of photons through space.
There are seven kinds of electromagnetic radiations in the
electromagnetic spectrum with varying photon energies.
They are gamma rays, X-rays, ultraviolet radiations, visible
light, infrared rays, microwaves, and radio waves.
3. Electromagnetic spectrum:
The electromagnetic spectrum is a continuum arrangement of
electromagnetic radiations. It is in the increasing order of their wavelengths
and with the decreasing order of their frequencies.
Additional reference:
A PowerPoint presentation on MCQs of Planck constant
4. Black body:
A black body absorbs all radiations incident on it
regardless of their frequencies and wavelengths.
5. Blackbody radiations:
On heating, the black body emits all the absorbed radiations
with wavelengths ranging from zero to infinity. These emitted radiations are
black body radiations.
6. Quantum:
A quantum is a particle of discrete energy that travels from
one point to another.
7. Photon:
The discrete chunks of light energy are known as a photon.
For the difference between a quantum and a photon, check out here.
8. Light energy
Light energy is a form of electromagnetic radiation that comprises photon particles.
The oscillations of electrically charged bodies produce it.
Their wavelengths lie in the visible region so the human eye can
observe them.
An infographic on light energy
Units of light energy:
The SI unit of photon energy is the joule.
Erg is the CGS unit of radiant energy.
In atomic units, electron volt (eV) expresses the light
energy.
9. Frequency:
Frequency defines the number of cycles or vibrations completed
in one unit time.
It is the number of waves that pass through a given point in
one second.
The Greek symbol γ denotes it.
Hertz is the unit of frequency in both the CGS and SI
systems.
Hertz is the inverse of a second.
Hertz = second-1 = 1/second
It is independent of the medium of propagation. Hence, it is a fixed quantity irrespective of the nature of the medium.
10. Wavelength:
It is the distance
between the two consecutive matching same phase points in the periodic motion
of a wave.
We measure it differently for transverse and longitudinal
waves.
It is the distance between the two adjacent crests or
troughs in a transverse wave motion.
It is the distance
between the centers of two successive compressions or rarefactions in a
longitudinal wave motion.
The Greek letter Lambda (λ) designates it.
Meter is the SI unit, and the centimeter is the CGS unit of wavelength.
Besides, the length units such as micrometer, nanometer, picometer, and angstrom express the wavelength.
But, the nanometer is the most commonly
used unit to measure the wavelength of electromagnetic waves.
11. Relationship between wavelength and frequency of electromagnetic radiation:
The product of wavelength and frequency is equal to the
velocity of light in a vacuum.
Velocity of light in vacuum = wavelength x
frequency
c= λ x ν
Where,
c is a constant quantity. It is the velocity of light in a
vacuum. And it is equal to 3 x 108 meters/second.
λ =
Wavelength of radiation
ν= Frequency of light
From the above relation, the frequency formula of
electromagnetic light is;
ν ∝ 1/λ
ν = c/λ
Similarly, the wavelength formula for electromagnetic light
is
Both the above equations prove that the wavelength and
frequency of light are inversely related to each other.
12. Wavenumber:
It defines the number of waves per unit distance.
And it is reciprocal to the wavelength of a wave.
The formula to calculate the wavenumber of a wave is;
Wavenumber = 1/ wavelength
Ῡ = 1/λ
The Greek symbol Ῡ (nu bar) denotes it.
And it is expressed as m-1 in SI units and cm-1
in CGS units.
13. Planck constant:
It is a fundamental physical quantity. It explains the particle nature of light on the atomic and sub-atomic levels.
It is a
number that helps to calculate the energy of light.
The symbol
"h" denotes it.
It shows
the proportionality relation of Planck's constant with the photon's energy and
frequency. The formula for Planck constant is
It is a
constant value that does not change with time. So, it is a universal constant.
Value of Planck constant:
The value
of Planck's constant is 6.626 X 10-34 joule second in the SI system.
In the CGS system, the value of Planck's constant is 6.626 X 10-27 erg second.
In atomic
units, the value of Planck's constant is
Planck quantum laws:
Planck quantum law gives the mathematical relations to calculate the wavelength, frequency, and wavenumber of electromagnetic radiations.
Planck quantum-frequency relation:
It states that the energy of a photon varies directly with its frequency.
According to this law, the radiation frequency computes the associated radiant energy.
E=nhν
So, low-frequency radiations contain low energy. Likewise, high energetic radiations possess high frequencies.
Planck quantum-wavelength relation:
It divulges that the energy of a photon varies inversely with the wavelength of light radiation.
Planck quantum wavelength relationship is E = hc/λ.
The mathematical formula expresses the quantum size from the wavelength of light.
Radiations
with longer wavelengths have lower energies. And shorter wavelength radiations
are highly energetic.
By filling h and c values in the above mathematical formula, we get;
E = (6.626 x 10-34)
x (3 x 108) /λ joules
E = 19.878 x 10-26
/λ joules
Planck quantum-wavenumber relation:
It
indicates the wavenumber of the light radiations varies directly with its
photon energy.
Planck quantum wavenumber relationship is E = hcῩ
Ῡ = E/hc
A photon
with a higher wavenumber has higher energy. Conversely, lower energy photon has
lower wavenumber.
By substituting the values of Planck's constant and the speed of light in a vacuum in the above mathematical formula, we get;
E=hcῩ
E= {(6.626 x
10-34) x (3 x 108) x Ῡ} joules
E= {(19.878 x
10-26) x Ῡ} joules
Multiple choice questions and answers of Planck quantum theory:
1. What is the motto of Planck's quantum
theory?
A. Electromagnetic character of light
B. Quantum phenomenon of radiant energies
C. Spin-angular momentum of electron
orbits
Answer:
Quantum phenomenon of radiant energies
2. Who demonstrated the wave character of
light?
A. Max Planck
B. James Clerk Maxwell
C. Christian Huygens
Answer:
Christian Huygens
3. Light possesses the dual character of
both particle and wave. Verify whether the above statement is true or false.
A. True
B. False
Answer:
True
4. Which of the following phenomenon obeys
the particle nature of electromagnetic energies?
A. Photoelectric effect
B. Blackbody
C. Both A and B
Answer: Both A and B
5. What is the character of light when it
propagates from water to air?
A.
Particle character
B. Wave character
C. Magnetic character
Answer:
Wave character
6. Which of the following technique of the
medical field follows Planck's quantum theory?
A. X-ray
B. MRI scan
C. Radiation therapy
Answer:
MRI scan
7. The following question consists of two
statements say assertion and explanation. Pick which of the mentioned option is
correct.
Assertion: Planck's constant is a
universal physical quantity
Explanation: It is a fixed numerical value
that is unchanged with time.
A. Both assertion and explanation are
correct.
B. Assertion is true. And the explanation
is false.
C. Assertion is false. And the explanation
is true.
Answer:
Both assertion and explanation are correct
8. Planck's constant measures
____________________
A. Angular frequency
B. Linear frequency
C. Momentum
Answer:
Linear frequency
9. By using the Planck quantum formula,
E=hν. Calculate the h value if the photon magnitude is 5-kilo joules and has a
wavelength of 250 nm.
A. 50 joule second
B. 6626 x 10-3 joule second
C. 6.626 x 10-34 joule second
Answer: 6.626 x 10-34 joule
second
10. What is the objective of Planck's
quantum theory?
A. Calculation of radiation frequencies
B. Studying the internal atomic structure
C. To prove the existence of energy
particle
Answer:
To prove the existence of energy particle
Overview of Planck's constant:
Planck's constant is a universal fixed physical quantity whose value is 6.626 x 10-34 joule seconds. And it helps to measure the size of the quantum from the known frequencies of emitted electromagnetic radiations. The physicist Max Planck invented it to measure the quantum magnitude of blackbody emissions. It is a brief description of Planck's constant. We have a fatafat checklist of Planck's constant. Let us have a look at it.
Fatafat checklist of Planck's constant:
i) What is Planck's constant?
It is a fixed number and a universal
constant.
ii) Why is it discovered?
To determine the magnitude of quantum.
iii) How is it denoted?
The English letter 'h' represents it.
iv) When was it invented?
In 1900
v) What is an experimental method to
determine h?
Kibble balance
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Numerical problems of Planck's constant:
Here is a PPT e-book of numerical problems on Planck's constant. Scroll right to see all the content.
To conclude, Planck's quantum theory helps calculate the
photon energies from the known data of wavelength, frequency, or wavenumber of
electromagnetic radiation. It assists in the identification of chemical
elements in unknown substances and celestial matter.
So, the Planck quantum model became the backbone of quantum
mechanics. And it led to further advancements in modern quantum physics.
What are the postulates of Planck's quantum theory?