Recent questions in Wien's displacement law

Quantum MechanicsAnswered question

crubats4b5p 2023-03-25

The velocity function is $$ for a particle moving along a line. What is the displacement (net distance covered) of the particle during the time interval [-3,6]?

Quantum MechanicsAnswered question

Will Hodges 2023-03-11

A passenger plane made a trip to Las Vegas and back. On the trip there it flew 432 mph and on the return trip it went 480 mph. How long did the trip there take if the return trip took nine hours?

Quantum MechanicsAnswered question

Jamari Bowman 2023-02-21

The position of an object moving along a line is given by $$. What is the speed of the object at $$?

Quantum MechanicsAnswered question

tisanurnr9c 2023-02-15

A person observes fireworks displays from the safe distance of 0.750 meters. Assuming that the sound travels at 340 meters per second in air. What is the time between the person seeing the fireworks and hearing the explosion?

Quantum MechanicsAnswered question

Heidy Haley 2023-02-08

What is the speed of a rocket that travels 9000 meters in 12.12 seconds?

Quantum MechanicsAnswered question

Camsassophy71s 2023-02-08

The distance between the earth and the moon is about 384,000 km. calculate the time it takes for light to travel from the moon to earth?

Quantum MechanicsAnswered question

Talan Mercer 2023-01-13

The velocity of the particle is given by v=3t^2+2t in m/s. The acceleration and displacement of the particle as a function of time respectively are...

Quantum MechanicsAnswered question

yegumbi4q0 2023-01-01

The transverse displacement y(x, t) of a wave on a string is given by $y(x,t)={e}^{(a{x}^{2}+b{t}^{2}+2\sqrt{ab}xt)}$. This represent:

A) wave moving in +x direction with speed $\sqrt{\frac{a}{b}}$

B) wave moving in +x direction with speed $\sqrt{\frac{b}{a}}$

C) standing wave of frequency $\sqrt{b}$

D) standing wave of frequency $\frac{1}{\sqrt{b}}$

A) wave moving in +x direction with speed $\sqrt{\frac{a}{b}}$

B) wave moving in +x direction with speed $\sqrt{\frac{b}{a}}$

C) standing wave of frequency $\sqrt{b}$

D) standing wave of frequency $\frac{1}{\sqrt{b}}$

Quantum MechanicsAnswered question

Marques Flynn 2022-12-01

A husband and wife take turns pulling their child in a wagon along a horizontal sidewalk. Each exerts a constant force and pulls the wagon through the same displacement. They do the same amount of work, but the husband's pulling force is directed ${58}^{o}$ above the horizontal, and the wife's pulling force is directed ${38}^{o}$ above the horizontal. The husband pulls with a force whose magnitude is 60 N. What is the magnitude of the pulling force exerted by his wife?

Quantum MechanicsAnswered question

blackdivcp 2022-10-16

The displacement of a particle at t = 0.350 s is given by the expression x = (3.00 m) \cos(6.00xt), where x is in meters and is in seconds (a) Determine the frequency and period of the motion Hz s (b) Determine the amplitude of the motion m (c) Determine the displacement of the particle at t = 0.350 s. m (d) At what time after t=0 does it first reach equillibrium? (e) At what time after t=0 does it reach zero velocity for the first time? (f)What total distance does it travel during the first period?

Quantum MechanicsAnswered question

William Santiago 2022-05-20

Landauer's principle vs Wien's displacement law

Can we argue based on Landauer's principle that if one bit information is changed inside a blackbody, the total radiated energy should be at least or in order of kTln2? If it is so, can we also argue that this energy should be distributed over all the modes of the cavity? Furthermore, can it also be argued that this contradicts with the Wien's displacement law which says the total energy should be in the order of $k\frac{{T}^{4}}{{h}^{4}}$ (as integrated using Mathematica 8.0)?

Can we argue based on Landauer's principle that if one bit information is changed inside a blackbody, the total radiated energy should be at least or in order of kTln2? If it is so, can we also argue that this energy should be distributed over all the modes of the cavity? Furthermore, can it also be argued that this contradicts with the Wien's displacement law which says the total energy should be in the order of $k\frac{{T}^{4}}{{h}^{4}}$ (as integrated using Mathematica 8.0)?

Quantum MechanicsAnswered question

Jordon Haley 2022-05-20

Wien's Displacement and Rayleigh-Jeans Law from Planck's Law

I've derived Planck's Law for frequency from his law for wavelength, and I got this:

$u(f)=\frac{8\pi {f}^{2}}{{c}^{3}}\frac{hf}{{e}^{\frac{hf}{kT}}-1}$

I just have a quick question about this. This problem says I need to find the low-frequency limit (which will lead to the Rayleigh-Jeans), and I need to take the high-frequency limit, which is supposed to lead to Wien's distribution.

The thing is I have no idea what the high, or low frequency limit even means, I've looked in my book, I've looked online, I'm not sure exactly what it means.

I've derived Planck's Law for frequency from his law for wavelength, and I got this:

$u(f)=\frac{8\pi {f}^{2}}{{c}^{3}}\frac{hf}{{e}^{\frac{hf}{kT}}-1}$

I just have a quick question about this. This problem says I need to find the low-frequency limit (which will lead to the Rayleigh-Jeans), and I need to take the high-frequency limit, which is supposed to lead to Wien's distribution.

The thing is I have no idea what the high, or low frequency limit even means, I've looked in my book, I've looked online, I'm not sure exactly what it means.

Quantum MechanicsAnswered question

Jaime Coleman 2022-05-20

How do we know that dark matter is dark?

How do we know that dark matter is dark, in the sense that it doesn't give out any light or absorb any? It is impossible for humans to be watching every single wavelength. For example, what about wavelengths that are too big to detect on Earth?

How do we know that dark matter is dark, in the sense that it doesn't give out any light or absorb any? It is impossible for humans to be watching every single wavelength. For example, what about wavelengths that are too big to detect on Earth?

Quantum MechanicsAnswered question

Iyana Macdonald 2022-05-20

How do you change Planck's law from frequency to wavelength?

I have to derive Wien's displacement law by using Planck's law. I've tried but I come to a unsolvable equation (well I can't solve it) anywhere I look online it comes to the same conclusion, you need to solve an equation involving transcendentals which I have no idea what they are nor any of the math classes required for this physics course teach it. Once that equation is solved, the next steps are quite simple, by using the solution.

Maybe my professor just wants us to google the solution to the equation and used it to keep solving the problem?

anyway, what really bothers me is this:

My book shows Planck's law in terms of frequency

${B}_{\nu}(T)=\frac{2h{\nu}^{3}}{{c}^{2}}\frac{1}{{e}^{h\nu /({k}_{B}T)}-1}$

but to do the problem I need it in terms of wavelength

${B}_{\lambda}(T)=\frac{2h{c}^{2}}{{\lambda}^{5}}\frac{1}{{e}^{hc/(\lambda {k}_{B}T)}-1}$

And $v=c/\lambda $, so by that then it can be said that the exponent of $\lambda $ would be 3 when it is expressed in terms of lambda (plus $c$ would have an exponent of 1). But Wikipedia says it is 5 and not 3. It multiplies by the derivative of $\nu $, but I don't get why. I'm just substituting, not differentiating, no need to use the chain rule.

I have to derive Wien's displacement law by using Planck's law. I've tried but I come to a unsolvable equation (well I can't solve it) anywhere I look online it comes to the same conclusion, you need to solve an equation involving transcendentals which I have no idea what they are nor any of the math classes required for this physics course teach it. Once that equation is solved, the next steps are quite simple, by using the solution.

Maybe my professor just wants us to google the solution to the equation and used it to keep solving the problem?

anyway, what really bothers me is this:

My book shows Planck's law in terms of frequency

${B}_{\nu}(T)=\frac{2h{\nu}^{3}}{{c}^{2}}\frac{1}{{e}^{h\nu /({k}_{B}T)}-1}$

but to do the problem I need it in terms of wavelength

${B}_{\lambda}(T)=\frac{2h{c}^{2}}{{\lambda}^{5}}\frac{1}{{e}^{hc/(\lambda {k}_{B}T)}-1}$

And $v=c/\lambda $, so by that then it can be said that the exponent of $\lambda $ would be 3 when it is expressed in terms of lambda (plus $c$ would have an exponent of 1). But Wikipedia says it is 5 and not 3. It multiplies by the derivative of $\nu $, but I don't get why. I'm just substituting, not differentiating, no need to use the chain rule.

Quantum MechanicsAnswered question

Blaine Stein 2022-05-18

What causes hot things to glow, and at what temperature?

I have an electric stove, and when I turn it on and turn off the lights, I notice the stove glowing.

However, as I turn down the temperature, it eventually goes away completely. Is there a cut-off point for glowing?

What actually is giving off the light? Does the heat itself give off the light, or the metal?

I have an electric stove, and when I turn it on and turn off the lights, I notice the stove glowing.

However, as I turn down the temperature, it eventually goes away completely. Is there a cut-off point for glowing?

What actually is giving off the light? Does the heat itself give off the light, or the metal?

Quantum MechanicsAnswered question

Marissa Singh 2022-05-18

Relationship between Wien's law and Stefan-Boltzmann's law

I'm studying Quantum mechanics by Bransden and Joachain and in the introduction chapter it says:

Wien showed that the spectral distribution function had to be on the form

$\rho (\lambda ,T)={\lambda}^{-5}f(\lambda T)$

where $f(\lambda T)$ is a function of the single variable $\lambda T$. It is a simple matter to show that Wien's law includes Stefan-Boltzmann law $R(T)=\sigma {T}^{4}$

One of the exercises is to show this and I cannot understand how to.

This is what I've tried:

The relationship between spectral emittance and spectral distribution is

$\rho (\lambda ,T)=\frac{4}{c}R(\lambda ,T),$

where c is the speed of light, which inserted in the above equation gives

$R(\lambda ,T)=\frac{c}{4}{\lambda}^{-5}f(\lambda T).$

Now, the total spectral emittance is the integral of $R$ over all wavelengths so

$R(T)=\frac{c}{4}\underset{0}{\overset{\mathrm{\infty}}{\int}}{\lambda}^{-5}f(\lambda T)d\lambda $

This is where I'm stuck. Can anyone help me figure this out?

I'm studying Quantum mechanics by Bransden and Joachain and in the introduction chapter it says:

Wien showed that the spectral distribution function had to be on the form

$\rho (\lambda ,T)={\lambda}^{-5}f(\lambda T)$

where $f(\lambda T)$ is a function of the single variable $\lambda T$. It is a simple matter to show that Wien's law includes Stefan-Boltzmann law $R(T)=\sigma {T}^{4}$

One of the exercises is to show this and I cannot understand how to.

This is what I've tried:

The relationship between spectral emittance and spectral distribution is

$\rho (\lambda ,T)=\frac{4}{c}R(\lambda ,T),$

where c is the speed of light, which inserted in the above equation gives

$R(\lambda ,T)=\frac{c}{4}{\lambda}^{-5}f(\lambda T).$

Now, the total spectral emittance is the integral of $R$ over all wavelengths so

$R(T)=\frac{c}{4}\underset{0}{\overset{\mathrm{\infty}}{\int}}{\lambda}^{-5}f(\lambda T)d\lambda $

This is where I'm stuck. Can anyone help me figure this out?

Quantum MechanicsAnswered question

Alissa Hutchinson 2022-05-15

Wien's displacement law in frequency domain

When I tried to derive the Wien's displacement law I used Planck's law for blackbody radiation:

${I}_{\nu}=\frac{8\pi {\nu}^{2}}{{c}^{3}}\frac{h\nu}{{e}^{h\nu /{k}_{b}T}-1}$

Asking for maximum:

$\frac{d{I}_{\nu}}{d\nu}=0:\text{}0=\frac{\mathrm{\partial}}{\mathrm{\partial}\nu}(\frac{{\nu}^{3}}{{e}^{h\nu /{k}_{b}T}-1})=\frac{3{\nu}^{2}({e}^{h\nu /{k}_{b}T}-1)-{\nu}^{3}h/{k}_{b}T\cdot {e}^{h\nu /{k}_{b}T}}{({e}^{h\nu /{k}_{b}T}-1{)}^{2}}$

It follows that numerator has to be $0$ and looking for $\nu >0$

$3({e}^{h\nu /{k}_{b}T}-1)-h\nu /{k}_{b}T\cdot {e}^{h\nu /{k}_{b}T}=0$

Solving for $\gamma =h\nu /{k}_{b}T$:

$3({e}^{\gamma}-1)-\gamma {e}^{\gamma}=0\to \gamma =2.824$

Now I look at the wavelength domain:

$\lambda =c/\nu :\text{}\lambda =\frac{hc}{\gamma {k}_{b}}\frac{1}{T}$

but from Wien's law $\lambda T=b$ I expect that $hc/\gamma {k}_{b}$ is equal to $b$ which is not:

$\frac{hc}{\gamma {k}_{b}}=0.005099$, where $b=0.002897$

Why the derivation from frequency domain does not correspond the maximum in wavelength domain?

I tried to justify it with chain rule:

$\frac{dI}{d\lambda}=\frac{dI}{d\nu}\frac{d\nu}{d\lambda}=\frac{c}{{\nu}^{2}}\frac{dI}{d\nu}$

where I see that $c/{\nu}^{2}$ does not influence where $d{I}_{\lambda}/d\lambda $ is zero.

When I tried to derive the Wien's displacement law I used Planck's law for blackbody radiation:

${I}_{\nu}=\frac{8\pi {\nu}^{2}}{{c}^{3}}\frac{h\nu}{{e}^{h\nu /{k}_{b}T}-1}$

Asking for maximum:

$\frac{d{I}_{\nu}}{d\nu}=0:\text{}0=\frac{\mathrm{\partial}}{\mathrm{\partial}\nu}(\frac{{\nu}^{3}}{{e}^{h\nu /{k}_{b}T}-1})=\frac{3{\nu}^{2}({e}^{h\nu /{k}_{b}T}-1)-{\nu}^{3}h/{k}_{b}T\cdot {e}^{h\nu /{k}_{b}T}}{({e}^{h\nu /{k}_{b}T}-1{)}^{2}}$

It follows that numerator has to be $0$ and looking for $\nu >0$

$3({e}^{h\nu /{k}_{b}T}-1)-h\nu /{k}_{b}T\cdot {e}^{h\nu /{k}_{b}T}=0$

Solving for $\gamma =h\nu /{k}_{b}T$:

$3({e}^{\gamma}-1)-\gamma {e}^{\gamma}=0\to \gamma =2.824$

Now I look at the wavelength domain:

$\lambda =c/\nu :\text{}\lambda =\frac{hc}{\gamma {k}_{b}}\frac{1}{T}$

but from Wien's law $\lambda T=b$ I expect that $hc/\gamma {k}_{b}$ is equal to $b$ which is not:

$\frac{hc}{\gamma {k}_{b}}=0.005099$, where $b=0.002897$

Why the derivation from frequency domain does not correspond the maximum in wavelength domain?

I tried to justify it with chain rule:

$\frac{dI}{d\lambda}=\frac{dI}{d\nu}\frac{d\nu}{d\lambda}=\frac{c}{{\nu}^{2}}\frac{dI}{d\nu}$

where I see that $c/{\nu}^{2}$ does not influence where $d{I}_{\lambda}/d\lambda $ is zero.

Quantum MechanicsAnswered question

Landon Mckinney 2022-05-15

Uses of Wien's law of displacement

Wiens's displacement law says

${\lambda}_{\text{max}}T=\text{a constant}$

So if I have the ${\lambda}_{\text{max}}$, I can find the temperature of a star. But if I have the temperature, is there any point in calculating ${\lambda}_{\text{max}}$? What information does that give us of the star, besides temperature?

Wiens's displacement law says

${\lambda}_{\text{max}}T=\text{a constant}$

So if I have the ${\lambda}_{\text{max}}$, I can find the temperature of a star. But if I have the temperature, is there any point in calculating ${\lambda}_{\text{max}}$? What information does that give us of the star, besides temperature?

When you are facing the challenges of the Wien's displacement law problems, the best solution is to work with examples that help to explain the majority of questions that you have. Quantum mechanics belong to one of the most difficult aspects of physics, which is why it is paramount to explore more than two different answers and compare things. Using Wien's displacement law, you can work with the relations and approach the black body radiation by focusing on the peaks as you check the temperature changes and emissions. Ensure to browse through the lab reports assignment help answers when researching.