energy per range dλ of wavelengths, where wavelength and frequency are relatedby f= c. Show that Planck's formula in terms wavelength is given by:dU 8rVhc 1phc/λk ₂I - 12³dλ=[Note: Don't worry if you're off by an overall minus sign.](b) Show that Wien's Law follows from the spectral energy density dU/dλ from (a).[Hint: Make use of the fact (not to be proven here) that the emission strength of ablack body at a given wavelength λ, is proportional to dUldλ.](c) Which is hotter: "red hot" or "white hot"? Explain your reasoning.(d) Estimate the surface temperature of the star Arcturus, one of the brightest in thenighttime sky, if the dominant wavelength (=wavelength of maximum emissionstrength) of light it emits is 676 nm. In 1893, physicist Wilhelm Wien showed that the wavelength of maximum thermalemission strength of electromagnetic radiation from a blackbody at temperature Tobeys:Amax T 2.898 mm.K.=This result, known today as Wien's Law, is very useful for, among other things, esti-mating the temperature of distant objects based on the color of light they emit.(a) Planck's spectral energy density function is usually written as an energy per rangedf of frequencies. Quite often, however, it is more convenient to express it as an

Answered: In 1893, physicist Wilhelm Wien showed…

Similar questions

ASK YOUR (a) What is the de Broglie wavelength (in m) of an electron moving at a speed of 3.03 x 104 m/s? (b) What is the de Broglie wavelength (in m) of an electron moving at a speed of 2.01 x 10° m/s? Need Help? Read It
In a photoelectric experiment using a sodium surface, you find a stopping potential of 1.86 V for a wavelength of 300 nm and a stopping potential of 0.885 V for a wavelength of 393 nm. From these data find (a) a value for the Planck constant, (b) the work function for sodium, and (c) the cutoff wavelength Ao for sodium. (a) Number i (b) Number i (c) Number i Units Units Units >
The intensity of blackbody radiation peaks at a wavelength of 583 nm. (a) What is the temperature (in K) of the radiation source? (Give your answer to at least 3 significant figures.) K (b) Determine the power radiated per unit area (in W/m2) of the radiation source at this temperature. W/m?
Planck’s constant has the value h = 6.626 × 10–34 joule-seconds (J-s), and the speed of light is c = 3 × 108 m/s. Using these values, calculate the wavelength carried by photons emitted with an energy of 1.1 × 10-19 J. Pick the closest value:
The work function of a tungsten surface is 5.4 eV. When the surface is illuminated by light of wavelength 175 nm, the maximum photoelectric energy is 1.7 eV. Find Planck's constant from these data.
(a) A vacuum photocell is sequentially illuminated with light of different wavelengths 2. A voltmeter is used to determine that there is a different voltage between the cathode and the anode. V (iii) Determine a relation for Planck's constant in terms of pairs of voltage measurements at different wavelengths such that W₁ cancels out. (iv) Evaluate Planck's constant for the following pair of measurements: measurement 1 finds = 447 nm and V=635 mV, and measurement 2 finds = : 502 nm and V=339 mV.
(b) Calculate the de Broglie wavelength of an electron having a mass of 9.11 x 10-31 kg and a charge of 1.602 x 10-19 J with a Kinetic energy of 110 eV. The value of the Planck’s constant is equal to 6.63 * 10-34 Js.
For a body emitting blackbody radiation, the total power emitted is proportional to the 4th power of the body’s absolute temperature:(T in kelvins)and the wavelength of the emitted EM radiation that has the highest intensity is inversely proportional to the body’s absolute temperature according to:( in meters, T in kelvins)Assume an object is emitting blackbody radiation. A body in a room at 300 K is heated to 3,000 K. The wavelength of the most intense EM radiation emitted by the body at 3,000 K is the wavelength of the most intense EM radiation at 300 K.
2.3. Find the de Broglie wavelength of (a) an electron, and (b) a proton with speeds of 5 × 106 m/s and compare with the radius of the hydrogen atom, ao. Would either of these particles behave like a wave inside the H atom?
Einstein won the Nobel Prize in physics for the photo-electric effect in 1924 for his interpretation of the photoelectric effect in a paper published in 1905 when he was 26 years old. This work resulted in the Einstein-Planck Equation for the energy of a photon: E = hv = (h/2n) 0 Similarly, Louis de Broglie, in his 1924 Ph.D. thesis proposed that just as light (and other electromagnetic waves) has both wave-like and particle-like properties, matter (and in particular electrons) has wave-like properties and that the momentum p of these matter waves have a momentum given by: p= h/2 = (h/2z)k, where, as in class, k = 2wn In both equations, h is Planck's constant = 6.62607004 x 1034 m²kg/s a) using Ao At = 1, show that AE At = (h/2n) b) using Az Ak = 1, show that Az Ap = (h/2R) c) Since momentum p = mass times velocity = mv, use another of Einstein's favorite equations, E = mc? to write p = E/c for a photon or electron, and using the Einstein-Planck Equation obtain de Broglie's formula for…