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Let λmax be the wavelength where the Planck distribution function has its maximum. Prove that λmaxT-const....
P7A.4 The wavelength λmax at which the Planck distribution is a maximum can be found by...
P7A.4 The wavelength λmax at which the Planck distribution is a maximum can be found by solving dp(AT)/d7-0. Differentiate ρα'T) with respect to T and show that the condition for the maximum can be expressed as xe 5(e-1) = 0, where x = hc/AKT. There are no analytical solutions to this equation, but a numerical approach gives x = 4.965 as a solution. Use this result to confirm Wien's law, that λmaxT is a constant, deduce an expression for the...
Calculate the maximum wavelength, ?max,λmax, of electromagnetic radiation that could eject electrons from the surface of...
Calculate the maximum wavelength, ?max,λmax, of electromagnetic radiation that could eject electrons from the surface of copper, which has a work function of 7.26×10^−19 J. ?max= __________ m If the maximum speed of the emitted photoelectrons is 2.06×10^6 m/s, what wavelength of electromagnetic radiation struck the surface and caused the ejection of the photoelectrons? ?= _____________ m
The maximum entropy distribution is Gaussian with two constraints. Use the Lagrange multiplier method to prove...
The maximum entropy distribution is Gaussian with two constraints. Use the Lagrange multiplier method to prove that the probability distribution pi that maximizes the entropy for die rolls, subject to a constant value of the second moment 〈i2〉, is a Gaussian function. Use εi = i. Two constraints:
7 (a)* The Planck constant h can be measured in an experiment using light-emitting diodes LEDs) Each LED used i...
7 (a)* The Planck constant h can be measured in an experiment using light-emitting diodes LEDs) Each LED used in the experiment emits monochromatic light. Te wavelength λ of the emitted photons is detemined during the manufacturing process and is provided by the manufacturer When the p.d. across the LED reaches a specific minimum value suddenly switches on emitting photons of light of wavelength the LED andi are related by the energy equation eVi hh flying lead Fig. 7.1 LED...
49. A normalized Lorentzian function may be written Its maximum value of 1/(π7) occurs at x-0. Th...
49. A normalized Lorentzian function may be written Its maximum value of 1/(π7) occurs at x-0. The half-width at half maximum is y. The area under the peak is unity (a) Prove the preceding statements. (b) Consider a dilute system of N oscillators per unit volume embedded in a dielectric medium. The oscillators have charge q, mass m, natural frequency ω oscillator strength fand damping time τ, where ωοτ > 1. The medium itself has no absorption near to, so...
Prove that the following two-point boundary-value problem has a UNIQUE solution. Thank you Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and...
Prove that the following two-point boundary-value problem has a
UNIQUE solution.
Thank you
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00<s< 00. Assume that on this domain THEOREM4 11. Prove that the following two-point boundary-value problem has a unique solution: "(t3 5)x +sin t
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00
(a) The elliptic equation in z and y is satisfied by the function ф(z,y) in the area S2. Prove th...
(a) The elliptic equation in z and y is satisfied by the function ф(z,y) in the area S2. Prove that a non-constant value of ф cannot assume a positive maximum or a negative minimurm inside of Ω where is negative. Hint: assume ф is maximal or minimal inside f . What does this imply about its derivatives there?
(a) The elliptic equation in z and y is satisfied by the function ф(z,y) in the area S2. Prove that a non-constant...
EXERCISE 4.16. Prove that every compact regular surface has a point of positive Gaussian curvature. HINT: LetpES be a point of maximum distance to the origin. By applying Exercise 1.43 on page 3...
EXERCISE 4.16. Prove that every compact regular surface has a point of positive Gaussian curvature. HINT: LetpES be a point of maximum distance to the origin. By applying Exercise 1.43 on page 32 to a normal section, conclude that the normal cur- vature of S at p in every direction is where r is the distance from p to the origin. EXERCISE 1.43 Let γ: 1 → Rn be a regular curve. Assume that the function t Iy(t) has a...
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer.
A random variable X has a distribution with probability function f(x) = K(nx)2x for x = 0,1,2,...,n where n is a positive integer. a. Find the constant k. b. Find the expected value M(S) = E(esX) as a function of the real numbers s. Compare the values of the derivative of this function M'(0) at 0 and the expected value of a random variable having the probability function above. c. What distribution has probability function f(x)? Let X1, X2 be independent random variables both...
Let fy(x, μ, σ) stand for the probability distribution function (PDF) for the normal distribution with...
Let fy(x, μ, σ) stand for the probability distribution function (PDF) for the normal distribution with parameters μ and σ. Let X be a random variable with a PDF defined as follows: where t is a fixed constant between O and 1. What is E[XI? None of these
P7A.4 The wavelength λmax at which the Planck distribution is a maximum can be found by solving dp(AT)/d7-0. Differentiate ρα'T) with respect to T and show that the condition for the maximum can be expressed as xe 5(e-1) = 0, where x = hc/AKT. There are no analytical solutions to this equation, but a numerical approach gives x = 4.965 as a solution. Use this result to confirm Wien's law, that λmaxT is a constant, deduce an expression for the...
7 (a)* The Planck constant h can be measured in an experiment using light-emitting diodes LEDs) Each LED used in the experiment emits monochromatic light. Te wavelength λ of the emitted photons is detemined during the manufacturing process and is provided by the manufacturer When the p.d. across the LED reaches a specific minimum value suddenly switches on emitting photons of light of wavelength the LED andi are related by the energy equation eVi hh flying lead Fig. 7.1 LED...
49. A normalized Lorentzian function may be written Its maximum value of 1/(π7) occurs at x-0. The half-width at half maximum is y. The area under the peak is unity (a) Prove the preceding statements. (b) Consider a dilute system of N oscillators per unit volume embedded in a dielectric medium. The oscillators have charge q, mass m, natural frequency ω oscillator strength fand damping time τ, where ωοτ > 1. The medium itself has no absorption near to, so...
Prove that the following two-point boundary-value problem has a
UNIQUE solution.
Thank you
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00<s< 00. Assume that on this domain THEOREM4 11. Prove that the following two-point boundary-value problem has a unique solution: "(t3 5)x +sin t
Theorem on Unique Solution, Boundary-Value Problem Let f be a continuous function of (t, s), where 0stSl and-00
(a) The elliptic equation in z and y is satisfied by the function ф(z,y) in the area S2. Prove that a non-constant value of ф cannot assume a positive maximum or a negative minimurm inside of Ω where is negative. Hint: assume ф is maximal or minimal inside f . What does this imply about its derivatives there?
(a) The elliptic equation in z and y is satisfied by the function ф(z,y) in the area S2. Prove that a non-constant...
EXERCISE 4.16. Prove that every compact regular surface has a point of positive Gaussian curvature. HINT: LetpES be a point of maximum distance to the origin. By applying Exercise 1.43 on page 32 to a normal section, conclude that the normal cur- vature of S at p in every direction is where r is the distance from p to the origin. EXERCISE 1.43 Let γ: 1 → Rn be a regular curve. Assume that the function t Iy(t) has a...
Let fy(x, μ, σ) stand for the probability distribution function (PDF) for the normal distribution with parameters μ and σ. Let X be a random variable with a PDF defined as follows: where t is a fixed constant between O and 1. What is E[XI? None of these
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