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How can you understand the particle in a box application of schrodingers equation in your physical world?
Well the particle in a box problem, which is described as a particle that is in a zero potential well whose walls have infinite potential. This would be like falling down a mine shaft with no way of getting out. Now what this problem helps us to understand is the probability attributes of quantum mechanics. We can find the expectation value for the position, in Dirac notation <psi | x | psi>, which will say that the most probable place that the particle is in the middle of the well (or box). Now just as an example, grab a marble and a cereal bowl (it must have a curved bottom). Now roll the marble down the side of bowl. Now glance at the bowl and look away. Make a note of where the marble is then do this a bunch of times and keep track of where the marble was every time you looked at it. If you were to plot these results you will find that even though the marble is always moving it spends most of it's time near the center of the bowl. Thus, you can accurately state that though the marble is not always at the center of the bowl the probability of it being near the center when you measure it's position (look at it) is higher than the probability of it being near the edges of the bowl! That is essentially what the particle in a box (infinite square well) problem is saying, with regards the the expectation value of position.
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What is the equation for lifetime of a particle?
The lifetime of a particle (τ) is related to its decay constant (λ) through the equation τ = 1/λ. The decay constant is inversely proportional to the half-life of the particle.
220 RN yields to alpha particle po-216 what particle or type of radiation needs to be included to balance the equation?
To balance the nuclear equation, a beta particle (negatron) must be included. The balanced equation would be 220/88 Ra -> 4/2 He (alpha particle) + 212/86 Rn + 2 -1 e.
What particle will balance the following nuclear?
Neutrons are the important particles of nuclear chain reactions
What does the coieffecient in a chemical equation tell you?
The number of that type particle involved in the reaction.
What happens to the energy of a particle if the mass is constant and the speed increases?
The kinetic energy of the particle increases as the speed increases, following the equation ( KE = \frac{1}{2} mv^2 ) where ( KE ) is the kinetic energy, ( m ) is the mass of the particle, and ( v ) is the speed of the particle. The energy of the particle is converted to kinetic energy as its speed increases.
Application of schrodinger equation to a particle in a box?
The Schrödinger equation describes how the quantum state of a physical system changes over time. For a particle in a one-dimensional box with infinitely high walls, the equation leads to quantized energy levels and wavefunctions that are confined within the box. The solutions reveal that the particle can only occupy specific energy states, with the wavefunctions exhibiting standing wave patterns. This model illustrates fundamental quantum concepts such as quantization and the probabilistic nature of particle position.
What is the equation for lifetime of a particle?
The lifetime of a particle (τ) is related to its decay constant (λ) through the equation τ = 1/λ. The decay constant is inversely proportional to the half-life of the particle.
What is the significance of the Smoluchowski equation in the study of Brownian motion and particle diffusion?
The Smoluchowski equation is important in studying Brownian motion and particle diffusion because it describes how particles move randomly in a fluid. It helps scientists understand how particles spread out and interact with each other, which is crucial in various fields such as chemistry, physics, and biology.
What is the significance of the Bethe Bloch equation in the field of particle physics and how is it used to describe the energy loss of charged particles in a material?
The Bethe Bloch equation is important in particle physics because it helps us understand how charged particles lose energy as they pass through a material. It describes the relationship between the energy loss of a charged particle and its velocity, charge, and the properties of the material it is passing through. By using this equation, scientists can predict and analyze the energy loss of charged particles in different materials, which is crucial for various applications in particle physics research and technology development.
What is the relationship between velocity and the magnetic field equation?
The relationship between velocity and the magnetic field equation is described by the Lorentz force equation. This equation shows how a charged particle's velocity interacts with a magnetic field to produce a force on the particle. The force is perpendicular to both the velocity and the magnetic field, causing the particle to move in a curved path.
What are the effects of particle size?
This depends on your problem or application.
220 RN yields to alpha particle po-216 what particle or type of radiation needs to be included to balance the equation?
To balance the nuclear equation, a beta particle (negatron) must be included. The balanced equation would be 220/88 Ra -> 4/2 He (alpha particle) + 212/86 Rn + 2 -1 e.
How can one derive the de Broglie equation from the principles of wave-particle duality?
To derive the de Broglie equation from the principles of wave-particle duality, one can consider that particles, like electrons, exhibit both wave-like and particle-like behavior. By applying the concept of wave-particle duality, one can relate the momentum of a particle to its wavelength, resulting in the de Broglie equation: h/p, where is the wavelength, h is Planck's constant, and p is the momentum of the particle.
What were erwin schrodingers biggest accomplishments?
Erwin Schrödinger is best known for his formulation of the Schrödinger equation, a fundamental equation in quantum mechanics that describes how quantum states evolve over time. He also contributed to the development of wave mechanics, establishing a wave-particle duality perspective on matter. Additionally, his thought experiment known as "Schrödinger's cat" illustrated the paradoxes of quantum superposition and measurement. Schrödinger received the Nobel Prize in Physics in 1933 for his pivotal contributions to the understanding of atomic and subatomic processes.
What is the nuclear decay equation for radium-288?
The equation for the beta decay of 24Na is: 1124Na --> 1224Mg + -10e where the e is a negative beta particle or electron.
What is the derivation of the de Broglie equation, which relates the wavelength of a particle to its momentum?
The de Broglie equation, which relates the wavelength of a particle to its momentum, is derived from the concept of wave-particle duality in quantum mechanics. It was proposed by Louis de Broglie in 1924, suggesting that particles, such as electrons, can exhibit wave-like properties. The equation is h/p, where is the wavelength, h is the Planck constant, and p is the momentum of the particle.
What is the nuclear decay equation for protactinium-231?
The equation for the alpha decay of 222Rn is: 86222Rn --> 84218Po + 24He Where He represents the alpha particle, which can also be viewed as a Helium nucleus.
