# Get help with nuclear quantum mechanics

Recent questions in Quantum Mechanics
Fescoisyncsibgyp8b 2022-05-13

### De-Broglie equation for other particles except photonIf E=hf is applicable for electron and other particles, the De Broglie wavelength should be λ=hv/pc. Because, mc^2=hf which implies mc^2=hc/λ which implies m=h/λc and thus λ=hv/pc. But I have found in my text book that λ=h/p is applicable not only for photon but also for all particle. But how can λ=h/p=h/mv be applicable for all particle?

vilitatelp014 2022-05-13

### Wavelength and relativityFrom de Broglie equation λ=h/p. But p=mv and velocity is a relativistic quantity so also wavelength is relative ? In other words does wavelength depends on the reference frame ?

studovnaem4z6 2022-05-13

### Special Relativity, Louis de Broglie Equation DilemmaWhile learning atomic structure I stumbled upon a very unusual doubt.As we know that the energy of a wave is given by the equation: $E=\frac{hc}{\lambda }$ and Louis de broglie wave equation is given by the equation ${\lambda }_{B}=\frac{h}{p}$. My doubt is that, that is ${\lambda }_{B}=\lambda$. Do the ${\lambda }_{B},\lambda$ represent the same thing $?$My teacher equated $E=\frac{hc}{\lambda }$ and $E=mc²$ to form $\frac{hc}{\lambda }=mc²$ and rearranged to form $\lambda =\frac{h}{mc}$ and then replaced $\lambda$ by ${\lambda }_{Β}$ and $c$ by $v$ for general formula and derived the Louis de broglie equation. This created my doubt in first place and I created another doubt that whether the equation for energy of wave is valid for relativistic equation of $E=mc²$ because the $E=mc²$ is for particles while the former is for waves.Is my understanding correct$?$ Please help and thanks in advance$!$

Jaiden Bowman 2022-05-10

### Wien's fifth power Law and Stephan Boltzmann's fourth power laws of emissive powerWien's fifth power law says that emissive power is proportional to the temperature raised to the fifth power. On the other hand, the Stefan–Boltzmann law says emissive power is proportional to the temperature raised to the fourth power. How can both of these be true?

hovudverkocym6 2022-05-10

### Wien's Displacement Law for real bodiesIt is known that for perfect blackbodies,$\lambda T=c$where $\lambda =\text{peak wavelength}$$T=\text{Absolute temperature}$$c=\text{Wien's constant}$But this is for perfect blackbodies only, which have no theoretical existence. Does a similar formula exist for real bodies, which expresses $\lambda T$ in terms of its emissitivity $ϵ$? I googled it, but found no relevant results.

Deshawn Cabrera 2022-05-09

### Area under Wien's displacement graphWhy does the area under Wien's displacement graph give Stefan-Boltzmann law for a black body?I couldn't find any proof of this. (I could just find this expression). I am not aware of the function of Wien's displacement graph as well (I just know that it is between Intensity and wavelength emitted by a black body).Is there a mathematical way to prove this?

bedblogi38am 2022-05-09

### Frequency and Wavelength peak for Wien's displaement law of a blackbody This is a question relating to Wien's displacement law for the Planck function. As we all know frequency and wavelength are related to the speed of light by:$\nu \lambda =c$However, why is it that:${\nu }_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}{\lambda }_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}\ne c$Any explanations would be very much appreciated.To all of the people wanting to know where this statement came from. It hasn't come from anywhere specific, is it a well known fact of the Planck function. ${\lambda }_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}=0.290{T}^{-1}$ cm K and ${\nu }_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}=5.88×{10}^{10}T$ Hz K${}^{-1}$

arbixerwoxottdrp1l 2022-05-09

### How can Wien's Displacement Law be 'changed' to a version for frequency?Wien's Displacement Law stated that for a blackbody emitting radiation,${\lambda }_{max}=\frac{1}{T}$where $T$ is the temperature of the body and ${\lambda }_{max}$ is the maximum wavelength of radiation emitted.Due to the relationship between wavelength, frequency and the speed of light, a value of maximum wavelength would give a value of minimum frequency, and vice versa.I then saw on the Wikipedia page for Wien's Displacement Law that${f}_{max}=\frac{\alpha {k}_{B}T}{h},$where $\alpha =2.82...$, ${k}_{B}$ is Boltzmann's Constant, $T$ is the temperature of the body and $h$ is Planck's Constant.How can this relationship for maximum frequency be shown?

Hailee Stout 2022-05-09

### Does the wavelenth of matter waves depend upon the kinetic energy of the particle or object?Do the properties of the waves (wavelength,frequency) emitted by a particle or object depend upon the velocity, or as to say its kinetic energy? Is the De Broglie equation $E=h\nu$ applicable to matter waves as well?

rynosluv101wopds 2022-05-08

### How to interpret the velocity in de Broglie's equation?Just wondering if anyone can help me understand the basic principle of quantum theory.De Broglie's equation allows one calculate the wave length of the physical object, following the fundamental wave-particle duality of quantum theory.$\lambda =h/mv$Since velocity $v$ is always relative to the reference frame of observer, does it imply that the wave property is not inherent but displays itself differently to different observers?

Brooklynn Hubbard 2022-05-08

### If a CMB photon traveled for 13.7 billion years (- 374,000 years) to reach me. How far away was the source of that CMB photon when it first emitted it?My attempt to solve this question was to use the following assumptions:1.Temperature of CMB photon today is 2.725 K (will use value of 3 K here)2.Temperature of CMB photon when it was first emitted is 3000 K3.A factor of x1000 in temperature decrease results in a factor of x1000 in wavelength increase. (According to Wien's displacement law)Does this mean that the source of the CMB photon that just reached me today, was actually 13.7 billion light years / 1000 = 13.7 million light years away from me when it first emitted the photon?

Kiersten Hodge 2022-05-08

### Importance of Schrodinger equation Louis de Broglie suggested that for microparticles like electrons, wave-like properties can be applied in order to explain some phenomena. Schrodinger wrote down an equation, a wave equation, describing these waves. What I do not understand is why is Schrodinger's contribution so important; if the concept of wave-like property of an electron was known already, then why writing a mere wave equation was an important step?

kwisangqaquqw3 2022-05-08

### De Broglie Wavelength interpretationI've just started learning about the double slit experiment (just in the short appendix section in Schroeder's Thermal Physics), and I'm extremely confused by this one thing:In it, out of basically nowhere he pulls out the De Broglie equation, that λ = h/p.I've studied double slit diffraction before, and I've been trying to connect them in order to understand what this wavelength actually means.In double slit diffraction, when the wavelength is larger, the diffraction "stripes" that form on the wall appear further apart. They also appear larger.y = $\frac{m\lambda L}{d}$ (approx, considering the distance to the screen is really large and thus almost parallel rays (drawn out waves) can have a path difference and interfere)If we were to make the wavelength extremely small, that would mean that anything a little off-center would interfere, so the smaller the wavelength, the closer together the "stripes" on the wall would be.Now, when we connect the 2 equations, this means that the faster the electrons are moving (the smaller their wavelength) the more places they will interfere on the wall, and therefore there will be a lesser distance between adjacent places where the electrons hit (bright spots) and places where they don't (dark spots).The way I'm interpreting this is that the smaller the "wavelength" of the electron, the more the probability it has to have been in different places at the same time, that is, the less we can know its position. That's why more stripes will appear on the detecting screen because there are more positions which the electron could've been in, and since its technically in all of them at the same time while it travels, it can interfere with itself more.Is this interpretation correct? Does a faster momentum (a smaller wavelength) mean that the electron literally is at more places at the same time while it travels from the electron gun, through the slits, and to the wall? Thank you!

Eve Dunn 2022-05-08

### Origin of the de Broglie EquationI was curious about the famous $p=\hslash k$ equation. In high school I think you are just exposed to this equation with the explanation of "something something matter waves." But early in a undergraduate QM course you solve the time-independent Schrodinger's equation for a free particle in 1D and get the following solution:$\frac{-{\hslash }^{2}}{2m}\frac{{\mathrm{\partial }}^{2}}{\mathrm{\partial }{x}^{2}}\psi =E\psi \phantom{\rule{thickmathspace}{0ex}}⟹\phantom{\rule{thickmathspace}{0ex}}\psi ={e}^{±ikx}$ and $E=\frac{{\hslash }^{2}{k}^{2}}{2m}$where I believe $k$ is just defined by the $E\left(k\right)$ equation. And then do we just realize that the $E\left(k\right)$ is the classical ${p}^{2}/2m$ equation if we set $p=\hslash k$, and thus we have "derived" $p=\hslash k$ or do we "know" $p=\hslash k$ beforehand and this just confirms it?

Stoyanovahvsbh 2022-05-08

### Why 8–15 µm is considered "thermal infrared" if typical room temperature kT is 48 µm?According to Wikipedia:"Long-wavelength infrared (8–15 µm, 20–37 THz, 83–155 meV): The "thermal imaging" region, in which sensors can obtain a completely passive image of objects only slightly higher in temperature than room temperature - for example, the human body - based on thermal emissions only and requiring no illumination such as the sun, moon, or infrared illuminator. This region is also called the "thermal infrared"."However, using $\frac{hc}{\lambda }={k}_{\mathrm{B}}T$, the temperature range 288–308 K (15–35 °C) is equivalent to 50–46.7 µm, while 8–15 µm is equivalent to 1800–960 K (using the same equation).

Annabel Sullivan 2022-05-08

### Is there a significant error in using De Broglie's equation for an electron at really high speed?I was wondering if using the De Broglie equation$\lambda =\frac{h}{p}$for object traveling at really high speeds would result in a significant error. For example if an object travelled at $0.02c$ would the error be negligible? How can I calculate the uncertainty in the result?

studovnaem4z6 2022-05-07

### Derivation of Wien's displacement lawI know this might be a silly question, but is it necessary to know Planck's Law in order to show that ${\lambda }_{max}\propto \frac{1}{T}$? If you set$u\left(\lambda ,T\right)=\frac{f\left(\lambda T\right)}{{\lambda }^{5}}$then$\frac{\mathrm{\partial }u}{\mathrm{\partial }\lambda }=\frac{1}{{\lambda }^{5}}\frac{\mathrm{\partial }f}{\mathrm{\partial }\lambda }-\frac{5}{{\lambda }^{4}}f=0$$\frac{\frac{\mathrm{\partial }f}{\mathrm{\partial }\lambda }}{f}=5\lambda$But I am stuck here because if I integrate the L.H.S.$\int \frac{\frac{\mathrm{\partial }f}{\mathrm{\partial }\lambda }}{f}d\lambda =\mathrm{log}\left(f\left(\lambda T\right)\right)=\frac{5}{2}{\lambda }^{2}$

Waylon Mcbride 2022-05-07

### Direction of momentum given by the de Broglie relation$p=mv$where $m$ is the mass of an electron, and $v$ is its velocity. In this case, since $v$ is a vector, it's clear that the momentum will be also a vector.However if the momentum is a vector quantity (and it is), what is the direction of the electron's momentum given by the de Broglie relation$p=h/\lambda \phantom{\rule{0ex}{0ex}}p=\hslash k$if the Planck constant $h$ is scalar and the wavelength $\lambda$ is also scalar. Similarly the reduced Planck constant $\hslash$ is scalar and the wavenumber $k=2\pi /\lambda$ is also scalar.

Quantum mechanics problems and solutions belong to one of the most complex aspects of Physics because it takes several disciplines to get things done. It is exactly why we have a plethora of different questions that are asked by engineers, designers, programmers, data scientists, and students who do not have sufficient skills in Physics. Take your time to study quantum mechanics examples and explore the answers that have been offered. There are also de Broglie equation problems that focus on the wave properties of matter and the nature of the electrons that will help you. If you need to experiment with the other types of Quantum Mechanics and explore the radiation physics, make sure to che