Tiểu luận hóa lượng tử: Thuyết lượng tử Planck và các bài tập liên quan

At the end of the 20th century, the physicalworld rested on two new pillars, Einstein's theory of relativity and Planck's quantum theory.The father of Quantum theory, who brought "light"

HUE UNIVERSITY THE UNIVERSITY OF EDUCATION CHEMICAL SCIENCE

ESSAY

TOPIC: “PLANCK'S THEORY QUANTUM AND RELATED

Hue, 5/2021

Quantum theory not only explains exactly the structure of matter that Democrit envisioned, butalso greatly determines the prosperity of mankind At the end of the 20th century, the physicalworld rested on two new pillars, Einstein's theory of relativity and Planck's quantum theory.The father of Quantum theory, who brought "light" to the microscopic world, just as Newtononce brought light to the macro world, was the physicist Max Planck, when he discovered that atthe microscopic level, the energy exchange does not take place continuously but discretely intiny packets called "quanta" This discovery - along with Einstein's discovery of the "wave andparticle" dual nature of light five years later - were the fundamental axioms for the quantumrevolution.

Planck's quantum theory - the starting point for other later theories It has profound andcomprehensive implications in many areas of present life and future development and is

discussed in all introductory courses in quantum mechanics So how is Planck's quantum theorystated, and how can related exercises be performed?

Therefore, I decided to choose the topic "Planck quantum theory and related exercises" tohelp you better understand it

Although the article has made a lot of efforts, there will be mistakes, hope you can help correct it so that you can complete the article better

Content

I. The historical origins of quantum theory

- Max Karl Ernst Ludwig Planck (April 23, 1858 – October 4,

1947) was a German physicist, considered the founder of

quantum mechanics and therefore one of the most important

physicists of 20th century He won the Nobel Prize in Physics in

1918

- Max Planck comes from an academic family His

great-grandfather Heinrich Ludwig Planck (1785–1831) and

grandfather Heinrich Ludwig Planck (1785–1831) were

professors of theology at Göttingen His father, Wilhelm Johann

Julius Planck (1817–1900), was a professor of law in Kiel and

Munich; His uncle Gottlieb Planck (1824–1907) was also a

lawyer, one of the main contributors to the creation of the

Department of Civil Law (Bürgerliches Gesetzbuch, abbreviated BGB)

- He was born on April 23, 1858 in Kiel, to Johann Julius Wilhelm Planck and his second wifeEmma Patzig (1821–1914); he had four siblings (Hermann, Hildegard, Adalbert and Otto), aswell as two half-siblings (Hugo and Emma) from Johann Julius Wilhelm Planck's previous wives

He lived his early years in Kiel until his family moved back to Munich There, he attendedMaximilian High School; one of his classmates was the founder of the German Museum Oskarvon Miller He graduated from high school at the age of 17

- Planck is very musically gifted He played the piano, organ, cello and received vocal training Hecomposed a song and a small opera (Operette, 1876) for his student union, the Music Club ofMunich But instead of studying music, he decided to study physics

- The professor of physics in Munich, Philipp von Jolly, advised him not to study the subjectbecause "in this field almost everything has been studied, and the rest is just to patch up a few

Max Panck (1858-1947)

unimportant gaps important" ("in dieser Wissenschaft schon fast alles erforscht sei, und es gelte,nur noch einige unbedeutende Lücken zu schließen") – a view represented by many physicists ofthe time Planck replied, "I do not cherish the desire to explore new lands but only to understandthe existing foundations of the physical sciences and, if possible, to go further" ("Ich hege nichtden Wunsch, Neuland" zu entdecken, sondern lediglich, die bereits bestehenden Fundamente derphysikalischen Wissenschaft zu verstehen, vielleicht auch noch zu vertiefen") And he began tostudy physics in 1874 at the University of Munich.

- Where Jolly, Planck conducted the only experiments in his entire life of research (on the diffusion

of hydrogen through heating of platinum); soon after, he switched to theoretical physics

- Planck went to Berlin for a year (1877-1878) to study with the famous physicists Hermann vonHelmholtz and Gustav Kirchhoff as well as the mathematician Karl Weierstra ß Planck recordedthe following about Helmholtz: " never prepared well, stammered, always miscalculated andbore the listener", and of Kirchhoff: " prepared the lesson well, though natural, dry andmonotonous" Despite this, he became very close friends with Helmholtz For the most part hetaught himself from the writings of Rudolf Clausius It was through this influence that his field ofstudy later became the theory of thermodynamics

- In October 1878, he finished his master's degree (Lehramtsexamen), and submitted his doctoralthesis in March 1879 entitled "Thesis on the second principle of thermodynamics" (Über denzweiten Hauptsatz der mechanischen Wärmetheorie) In June 1880, he submitted his post-doctoral thesis (Habilitationsschrift) entitled "Equalization of isotropic bodies at differenttemperatures"

II. History of Max Planck

-Born in 1858, Max Planck came from an academic family His father Julius Wilhelm Planck wasProfessor of Law at the University of Kiel, Germany, and both his grandfather and great-grandfather had been professors of theology at Göttingen

-He received his doctorate in July 1879 at the age of 21 submitting a thesis on the second law ofthermodynamics

-While in Berlin, he became fascinated by the way energy from hot objects was emitted invariable quantities depending upon wavelength A number of physicists had tried to find amathematical description but no one had been totally

successful By combining equations derived by Wien and

Rayleigh, in October 1900 Planck announced a result now

known as Planck's radiation formula

- Planck himself said that: despite having invented quantum theory but he did not understand ithimself at first Nevertheless, he received the Nobel Prize for Physics in 1918 for hisachievement.

-Planck was 42 years old when he made his historic quantum announcement, but took only aminor part in the further development of quantum theory This was left to Einstein, Poincaré,Bohr, Dirac and others He died in October 1947

-Named in his ESA’s Planck mission is now analysing the Cosmic Microwave Backgroundradiation, which was formed soon after the Big Bang The data Planck collects will allowastronomers to search for clues about how galaxies form and cluster together, giving us thelarge-scale structure we see around us in space today

III Scientists' evaluations of Planck's quantum theory

-The story of the quantum theory begins with Max Planck, whose pioneering studies of thenature of radiation marked the end of what James Jeans called the “mechanical age of science”and ushered in a new era of discoveries that shook the very foundations of classical physics

-According to the Danish physicist Niels Bohr, Planck’s quantum theory “brought about a radicalrevolution in the scientific interpretation of natural phenomena [because] the picture of theuniverse formed on the lines of quantum physics must be looked upon as a generalization that isindependent of classical physics, with which it compares favorably for its beauty of conceptionand the inner harmony of its logic.”

- Werner Heisenberg, the discoverer of the uncertainty principle, was equally lavish in his praise

of Planck’s work: “At the time he [Planck] could scarcely have foreseen that within a span ofless then thirty years this theory, which flatly contradicted the principles of physics hithertoknown, would have developed into a doctrine of atomic structure which, for its scientificcomprehensiveness and mathematical simplicity, is not a whit inferior to the classical scheme oftheoretical physics.”

- Albert Einstein wrote that Planck’s work “has given one of the most powerful of all impulses tothe progress of science,” an impulse that Einstein believed would be effective “as long asphysical science lasts.”

IV The content of quantum theory Planck

1.1 Planck's Quantum Theory

According to Planck’s quantum theory,

-Different atoms and molecules can emit or absorb energy in discrete quantities only The

smallest amount of energy that can be emitted or absorbed in the form of electromagnetic

radiation is known as quantum.

-The energy of the radiation absorbed or emitted is directly proportional to the frequency of theradiation

-Meanwhile, the energy of radiation is expressed in terms of frequency as,

E = hvWhere,

E = Energy of the radiation

h = Planck’s constant (6.626×10–34 J.s)

v = Frequency of radiation

-Interestingly, Planck has also concluded that these were only an aspect of the processes ofabsorption and emission of radiation They had nothing to do with the physical reality of theradiation itself Later in the year 1905, famous German physicist, Albert Einstein alsoreinterpreted Planck’s theory to further explain the photoelectric effect He was of the opinionthat if some source of light was focused on certain materials, they can eject electrons from thematerial Basically, Planck’s work led Einstein in determining that light exists in discrete quanta

of energy, or photons

-Planck's quantum theory explains emission and absorption of radiation Postulates of Planck'squantum theory are as follows:

+ Matter radiate energy or absorb energy in discrete quantities discontinuously in the form of

small packets or bundles

+ The smallest bundle or packet of energy is known as quantum In case of light, a quantum of

light is known as a photon

+ The energy of the quantum absorbed or emitted is directly proportional to the frequency of the

radiation So, energy of the radiation is expressed in terms of frequency as follows- (Image to beadded soon)

+ A body or matter can radiate energy or absorb energy in whole number multiples of a quantum

as nhv Where n is a positive integer

1.2

Black body radiation

- Solids, when heated, emit radiation varying over a wide range of wavelengths For example:when we heat solid colour, changes continue with a further increase in temperature Thischange in colour happens from a lower frequency region to a higher frequency region as thetemperature increases

- For example, in many cases, it changes from red to blue An ideal body which can emit andabsorb radiation of all frequencies is called a black body The radiation emitted by such bodies

is called black body radiation Thus, we can say that variation of frequency for black bodyradiation depends on the temperature At a given temperature, the intensity of radiation isfound to increase with an increase in the wavelength of radiation which increases to amaximum value and then decreases with an increase in the wavelength This phenomenoncouldn’t be explained with the help of Maxwell’s suggestions Hence, Planck proposedPlanck’s quantum theory to explain this phenomenon

Example of black body radiation: the sun; a hot piece of metal;

Figure H.1: The light emitted by the sun (in yellow)

Matches the black body spectrum for 5778K

- Planck proposed that the vibrational energies of the atoms are quantized

- Planck’s expression for black body radiation :

E = Energy of the radiation

h = Planck’s constant (6.626×10–34 J.s)

v = Frequency of radiation

n = value results in quantization

- Planck's law describes electromagnetic radiation emitted by a black body in thermalequilibrium at a definite temperature The law is named after Max Planck, a physicist whoproposed it in 1900 This law was the first pioneering step in modern physics and quantummechanics

For frequency ν, or wavelength λ, Planck's law is written as:

B

2 hv 2

k T

2πv hv E(v,T)=

Figure H.2: The intensity of blackbody radiation versus the wavelength of the emitted

radiation Each curve corresponds to a different blackbody temperature, starting

with a low temperature (the lowest curve) to a high temperature (the highest curve).

1.3 Photoelectric effect

- Planck's three experimental observations that explain the photoelectric effect:

When light of a certain frequency shines on a clean metal surface, electrons are ejectedd fromthe metal Experimentally, it is found that:

+ The number of electrons ejected is proportional to the intensity of light

+ The kinetic energy of the ejected electrons is proportional to the frequency of the ejectedlight

+ No electrons can be ejected if the frequency of the light is lower than a certain value, calledthe threshold frequency ( 0

2. Planck’s expression for black body radiation

E = nhv (where n is an integral multiple)

This formula can also be written as:

nhc

E = λ

(Because we know frequency = speed of light/wavelength)

c

v = λ

3. Planck distribution for Black body radiation

B

2 hv 2

k T

2πv hv E(v,T)=

hc 6.626E

100 J s

= 2.012 × 10 s4.969 10 J×

11

Question 3: What is the energy of 5 mole of photons with a wavelength of 240 nm ?

Question 4: A 100-watt bulb emits monochromatic light of wave length 400 nm.

Calculate the number of photons emitted per second by the bulb

Question 5: The value of Planck’s constant is 6.63 × 10-34 J s The speed of light is

3 × 1017 nm s-1 Which value is closest to the wavelength in nanometer of a quantum

of light with frequency of 6 × 1015 s-1?

1.89×10 J

=4.99×10 photons 3.79×10 J

Question 9: Calculate the energy of the blue photon

Blue light is part of the visible light that the human eye can perceive Its length

oscillates between 400 nm and 475 nm, corresponding to greater or lesser energy

intensity Choose the one with the longest wavelength for exercise

Applying Planck’s formula

8

14 -1 -7

λ

c 3.00

v 1.025

×10 m/s

×10 = 2.968×1

-21 22

800

Question 12: Calculate and compare the energies of two radiation one with a

wavelength of 800 nm and other with of 400 nm

400Ratio of energy of first and second radiation

-1 9 1

2

9 -1

Question 14: Excited carbon atoms can emit photons with a wavelength of 150 nm

Calculate the total energy of the photons emitted by 30 g of carbon.

-34 8 -9 -18

6

hc 6.626×10 (3×10 m/s)E= =

λ 150×10 mE=1.325×10 J/photon30g C 1mol C 1mol photons 6.022×10 photons 1.325×10 J

Question 15: A Green light has a wavelength of 525nm Determine the energy for the

green light in joules

Question 16: The work function of copper metal is = 7.53 10-19 J If we shine light with a frequency of 3.0×1016 Hz on copper metal, will the photoelectric

effect be observed?