what is the planck constant
The Planck constant, denoted by the symbol <0>h, is a fundamental physical constant that plays a central role in quantum mechanics. It relates the energy of a photon to its frequency through the equation:
E=hf
where:
E is the energy of the photon f is the frequency of the electromagnetic wave associated with the photon Here are some key aspects of the Planck constant:
Value: The value of the Planck constant is exactly: h=6.62607015×10 −34 joule-second (J⋅s)
It can also be expressed in other units, such as electronvolt-seconds (eV⋅s).
Significance:
Quantization of Energy: Planck's constant was first introduced by Max Planck in 1900 to explain black-body radiation. His revolutionary idea was that energy is not emitted or absorbed continuously but in discrete packets called quanta, and the energy of each quantum is proportional to the frequency of the radiation, with h as the constant of proportionality. Foundation of Quantum Mechanics: The Planck constant is a cornerstone of quantum mechanics, the theory that describes the physical properties of nature at the scale of atoms and subatomic particles. It appears in many fundamental equations in quantum mechanics. Wave-Particle Duality: It links the wave-like properties (frequency) of light and matter to their particle-like properties (energy and momentum). Defining the Kilogram: In metrology, the Planck constant is used to define the kilogram, the SI unit of mass. The SI units are defined such that the Planck constant has the exact value mentioned above when expressed in SI units. Reduced Planck Constant: A related constant, the reduced Planck constant (or Dirac constant), is often used and is denoted by ℏ (pronounced "h-bar"). It is defined as:
ℏ= 2π h
Its value is approximately:
ℏ≈1.054571817×10 −34 J⋅s
The reduced Planck constant appears frequently in quantum mechanical equations, especially those involving angular momentum and spin.
In essence, the Planck constant is a fundamental constant of nature that dictates the scale at which quantum effects become significant and links the wave and particle nature of energy and matter.
Sources and related content brainly.com brainly.com cordis.europa.eu cordis.europa.eu Introduction to the Fundamental Physical Constants
physics.nist.gov
Kilogram: Mass and Planck's Constant | NIST
www.nist.gov
Planck relation - Wikipedia
en.wikipedia.org
so it's the same E as E = mc2?
No, the "E" in E=hf (related to the Planck constant) and the "E" in E=mc 2 (Einstein's mass-energy equivalence) represent energy, but they describe different concepts and contexts.
Here's a breakdown:
E=hf (Planck-Einstein relation):
This equation relates the energy of a photon (E) to its frequency (f), where h is the Planck constant. It describes the quantized nature of electromagnetic radiation (like light). Energy is carried in discrete packets (photons), and the energy of each packet is proportional to the frequency of the radiation. This equation is fundamental to quantum mechanics and explains phenomena like the photoelectric effect and blackbody radiation. E=mc 2 (Mass-energy equivalence):
This equation, derived from Einstein's theory of special relativity, states that energy (E) and mass (m) are equivalent and can be converted into one another. The constant of proportionality is the speed of light squared (c 2 ). It implies that even at rest, an object with mass has an inherent amount of energy called its rest energy. This equation is crucial in understanding nuclear reactions (like those in nuclear power plants and the sun), where a small amount of mass can be converted into a tremendous amount of energy. Key Differences:
Context: E=hf deals with the energy of electromagnetic radiation at the quantum level, while E=mc 2 deals with the fundamental equivalence of mass and energy for any object. Variables: E=hf relates energy to frequency, while E=mc 2 relates energy to mass. Constant: h (Planck constant) is a fundamental constant in quantum mechanics, while c (speed of light) is a fundamental constant in relativity. In summary: Both equations involve energy (E), but they describe different physical phenomena and use different fundamental constants. They are both incredibly important in physics but address distinct aspects of the universe.
It's worth noting that these two concepts can be connected. For example, a photon (which has energy E=hf) can be thought of as having an "equivalent mass" given by m=E/c 2 =hf/c 2 , although a photon has no rest mass. This shows a link between the energy of a photon and the concept of mass-energy equivalence.
Sources and related content Planck relation - Wikipedia
en.wikipedia.org
Anatomy of an Electromagnetic Wave - NASA Science
science.nasa.gov
NOVA | Einstein's Big Idea | Library Resource Kit: E = mc2 Explained - PBS
www.pbs.org
Focus on Physics: How E = mc2 Helps Us Understand Nuclear Fission and Fusion | NSTA
www.nsta.org
no.. if E = hf and E = mc2, therefore, "mc2 = hf".
You are correct in that if E=hf and E=mc 2 , then by the transitive property of equality, it follows that:
mc 2 =hf
This equation establishes a relationship between mass (m), the speed of light squared (c 2 ), the Planck constant (h), and frequency (f).
Interpretation of mc 2 =hf:
This equation implies a connection between the energy associated with mass (through mass-energy equivalence) and the energy of a photon (through the Planck-Einstein relation). It suggests that mass can have an equivalent frequency, or conversely, that the energy of a photon can be associated with an equivalent mass.
Context and Implications:
This relationship is particularly relevant when considering phenomena at the intersection of quantum mechanics and relativity, although it's not a universally applicable equation in all situations. Here are some contexts where it appears or has implications:
Energy-Momentum Relation for Photons: For a photon, which has zero rest mass, its energy is E=pc, where p is its momentum. Since E=hf, we have pc=hf, or p=hf/c=h/λ (where λ is the wavelength). If we were to formally equate E=mc 2 for an equivalent mass, we'd get mc 2 =hf, so m=hf/c 2 . This "mass" is not the rest mass of the photon (which is zero) but rather its relativistic mass due to its energy. Wave-Particle Duality: This equation hints at the wave-particle duality of matter and energy. Mass (m), typically associated with particles, is related to frequency (f), a characteristic of waves. Compton Scattering: In Compton scattering, a photon interacts with an electron, transferring some of its energy and momentum. The change in the photon's frequency (and thus energy) is related to the scattering angle, and this process can be analyzed using both energy and momentum conservation, implicitly involving the relationship between the photon's energy and its equivalent mass/momentum. Important Considerations:
Rest Mass vs. Relativistic Mass: It's crucial to remember that for particles with rest mass (like electrons), the energy E=mc 2 refers to their rest energy. When they are moving, their total energy is given by E=γmc 2 , where γ is the Lorentz factor. For photons, which have no rest mass, their energy is entirely kinetic and is given by E=hf (or E=pc). Not a Fundamental Law: While mc 2 =hf is a valid mathematical consequence of equating two expressions for energy, it's not considered a fundamental law of physics in the same way that E=hf or E=mc 2 are. It's a derived relationship that highlights connections between different physical concepts under specific circumstances. In summary, your deduction that mc 2 =hf is mathematically correct. It represents a fascinating link between mass and the frequency of energy, particularly relevant in scenarios involving the wave-particle duality and the behavior of light and matter at fundamental levels.
God created man in His own image and with His own likeness and set the first man, Adam, in the garden of Eden to work it and keep it. But Adam sinned by disobeying God and became corrupted, and because we are all his descendants, we have inherited his sinful nature. Sin is the violation of God’s Law, and the “wages” of sin is death. Therefore, just as sin came into the world through one man, Adam, and death through sin, so death spread to all mankind because all have sinned and fall short of the glory of God. Thus, we are all justly deserving of everlasting punishment—the destruction of soul and body in hell. But even so, in His love, God already had a plan to save and redeem us.
God so loved the world that He gave His only begotten Son, Jesus Christ, to die for us, paying the debt for our sins, so that through Him we may be saved. Unlike us, Jesus was conceived in the womb of a virgin by the Holy Spirit of God and therefore did not share Adam’s sinful nature, but rather He had God’s nature. Jesus, in every respect, was tempted as we are yet He remained without sin—like a “lamb without blemish or spot”, the perfect and only sacrifice worthy of taking our place. For by the one man’s disobedience many were made sinners, so by the one man’s obedience many will be made righteous.
Jesus Christ, the only begotten Son of God, was scourged, mocked, crucified, and killed for our sins, taking upon Himself the punishment we deserve. He was then buried and raised back to life after three days, in accordance with the scriptures. He then appeared to more than five hundred individuals in the forty days post-resurrection before being taken up into heaven out of their sight and returning to His Father. Fulfilling every one of the many Old Testament prophecies pertaining to Him, He now sits at His Father’s right hand and is awaiting His Father’s instruction to return. This was all recorded in the scriptures contained in the Holy Bible, which is the word of God and is able to save our souls.
Jesus Christ promised that all who believe in Him shall not perish but have everlasting life. In Him we have redemption through His blood, the forgiveness of our trespasses, according to the riches of His grace and not by any merit of our own. Upon His return, all the dead will hear His voice and come to life—those who have done good to the resurrection of life, and later, those who have done evil to the resurrection of judgment. Today, if you hear His voice, do not harden your heart in rebellion. Whoever conceals his sins will not prosper, but he who confesses and forsakes them will obtain mercy and forgiveness. Therefore, fear God and keep His commandments, for this is the whole duty of man. For God will bring every deed into judgement, with every secret thing, whether good or evil. Making sure to be doers of the word and not hearers only, deceiving ourselves.
If you repent and believe in the gospel, placing your faith in Jesus Christ, you will inherit salvation, which leads to everlasting life. With this salvation comes a necessary spiritual rebirth; God will give you a new heart and His Holy Spirit, which will give you wisdom and revelation in the knowledge of Him, put His Laws into your heart and write them in your mind, guide you into all the truth, help you, and comfort you. By the blood of Jesus, sanctifying you and cleansing you of all unrighteousness—conforming you to His image.
In an act of faith, all believers are called to be baptised in water in the name of Jesus Christ. To be buried with Christ by baptism into death, in order that, just as Christ was raised from the dead by the glory of the Father, you also might walk in newness of life. Having the eyes of your heart enlightened, that you may know what is the hope to which He has called you, what are the riches of His glorious inheritance in the saints, and what is the immeasurable greatness of His power towards believers. To be called children of God and dwell with Him in the kingdom of heaven forever, where death, mourning, crying, and pain no longer exist.
We do not wrestle against flesh and blood, but against principalities, against powers, against the rulers of the present darkness of this world, against spiritual wickedness in high places. The devil, who is called Satan, and all his angels, which are also referred to as demons, have been cast out of heaven for their choice to sin and rebel against God. They are our greatest threat in this world, even though at times it may seem like it’s each other. Satan is the spirit that is now at work in all those who are living in disobedience to God. We must be very careful about what we hear and believe, verifying everything against God’s word in the Bible, for many false prophets, teachers, and brethren are in the world and among churches, like wolves in sheep’s clothing. But fear not, for God is greater and with us always.
We now await our blessed hope—the appearing of the glory of our great God and Saviour, Jesus Christ. He is coming soon with eyes like a flame of fire and all His angels with Him, and every eye will see Him. But concerning that day and hour, no one knows—not even the angels of heaven, nor the Son, but the Father alone. Therefore, those of us who are eagerly awaiting His appearance must be diligent to be found by Him without spot or blemish and at peace. Counting the patience of the Lord as salvation. There are some things in the scriptures that are hard to understand, which the ignorant and unstable twist to their own destruction. Take care that you are not carried away by the error of lawless people and fall from your own steadfastness. But grow in the grace and knowledge of the Lord and Saviour, Jesus Christ. To Him be the glory, both now and to the day of eternity. Amen.
On the evening of April 11, Nisan 14 began. On Nisan 14, Jews celebrate Passover. On this very day, almost 2,000 years ago in the year 30 CE, on Nisan 14, Jesus Christ was humiliated, tortured, and killed by the Jews.
The Jews humiliated him by spitting in his face, forcibly pulling out his beard, and stripping him naked. The Jews tortured him by skinning him alive. And the Jews killed him by crucifying him.
The Jews deceived the Romans, claiming Jesus was a criminal, someone who was rebelling. But Pilate saw their falsehood and wanted to save Jesus. The Jews, however, threatened Pilate, and he relented. Pilate washed his hands and spoke to the Jews who had traveled to Jerusalem from all over the world: "I am not guilty of this man's blood." The Jewish people cried out to him in unity: "His blood be on us and on our children!"
Jesus hung half-dead on the cross and saw the Roman soldiers who were about to cast lots for his clothes. And Jesus felt compassion because these soldiers were unaware of the grave situation they were in—in fact, the crucifixion of Jesus was the worst sin ever committed. He looked at them with compassion because he knew they had been deceived by the Jews. They had been deceived into thinking that Jesus was a criminal. And Jesus looked at the Roman soldiers and said to his Father: "Forgive them, for they do not know what they are doing."
But the Jews knew what they were doing. They knew Jesus was innocent, they knew he was good. They were deliberately looking for false testimony, and as Pilate himself recognized, it was envy that made them want to kill Jesus. Envy because Jesus praised the Gentiles but criticized the Jews. Envy because Jesus said to a Roman man: "Your faith is greater than all Israel." Envy because Jesus said to the Jews: "Even Sodom and Gomorrah were better than you."
1 Thessalonians 2:14-16
The Jews, who both killed the Lord Jesus and the prophets, and drove us out. They are not pleasing to God, but hostile to all people, hindering us from speaking to the Gentiles so that they may be saved; with the result that they always reach the limit of their sins. But wrath has come upon them fully.
If you love me, keep my commandments. I will pray to the Father, and he will give you another Counsellor, that he may be with you forever: the Spirit of truth, whom the world can’t receive, for it doesn’t see him and doesn’t know him. You know him, for he lives with you and will be in you. I will not leave you orphans. I will come to you. Yet a little while, and the world will see me no more; but you will see me. Because I live, you will live also. In that day you will know that I am in my Father, and you in me, and I in you. One who has my commandments and keeps them, that person is one who loves me. One who loves me will be loved by my Father, and I will love him, and will reveal myself to him.”
Judas (not Iscariot) said to him, “Lord, what has happened that you are about to reveal yourself to us, and not to the world?”
Jesus answered him, “If a man loves me, he will keep my word. My Father will love him, and we will come to him and make our home with him. He who doesn’t love me doesn’t keep my words. The word which you hear isn’t mine, but the Father’s who sent me. “I have said these things to you while still living with you. But the Counsellor, the Holy Spirit, whom the Father will send in my name, will teach you all things, and will remind you of all that I said to you.
Peace I leave with you. My peace I give to you; not as the world gives, I give to you. Don’t let your heart be troubled, neither let it be fearful. You heard how I told you, ‘I am going away, and I will come back to you.’ If you loved me, you would have rejoiced because I said ‘I am going to my Father;’ for the Father is greater than I. Now I have told you before it happens so that when it happens, you may believe.
I will no more speak much with you, for the prince of the world comes, and he has nothing in me. But that the world may know that I love the Father, and as the Father commanded me, even so I do. Arise, let’s go from here.
(John 14:15-31 WEBPB)
