For a black body, the temperature and the wavelength of the emission maximum, Amax, are related by Wein's Law, expressed as: T/°C λmax/nm Values of Amax from a small pinhole in an electrically heated container were determined at a series of temperatures. The results are given below. Deduce the value of Planck's constant. 1000 2181 c = 3.00 x 108 m/s 1500 1600 hc 4.965k AmaxT=- 2000 1240 k= 1.38 x 10-34J.s 2500 1035 3000 878 3500 763
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- : In class we did a problem where we saw that Planck’s law, which is given byI(λ, T) = 2πhc2λ5(ehc/λkbT − 1),at high wavelengths reduces to the classical predictionI(λ, T) = 2πckBTλ4.We did this by using the MacLaurin series for an exponential.1 + x +x22! +x33! +x44! + ...When we did this problem in class, we reasoned that,when the wavelength (λ) is large, the term hc/λkbTis small enough that any term (hc/λkbT)2 or (hc/λkbT)3 or any higher power is neglible. That’s how weshowed that, in the limit of large λ, Planck’s law reduces to the classical prediction. Now assume that wewant to make a slightly better approximation. We still assume that λ is large and therefore (hc/λkbT)3 and(hc/λkbT)4 and all higher powers are negligible, but now we want to work at the level of precision where(hc/λkbT)2is not negligible. What does Planck’s law reduce to in this case?4. In an experiment on the photoelectric effect, a metal is illuminated by visible light of different wavelengths. A photoelectron has a maximum kinetic energy of 0.9 eV when red light of wavelength 640 nm is used. With blue light of wavelength 420 nm, the maximum kinetic energy of the photoelectron is 1.9 eV. Use this information to calculate an experimental value for the Planck constant h. [What temperature, in °C, is a blackbody whose emission spectrum peaks at 320 nm ? T= Submit Request Answer Part B VE ΑΣΦ T= Submit What temperature, in °C, is a blackbody whose emission spectrum peaks at 4.60 m? VE ΑΣΦ P By Request Answer ? Stag °C ? °C
- (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.For light with a wavelength of 350 nm and with an intensity of /= 10-8 W/m², what is the number of photons/(m²s) in the light beam?Calculate the de Broglie wavelength of an electron moving with 1/3rd of the speed of light in vacuum. (Neglect relativistic effect) (Planck's constant : h = 6.63 × 10-34 Js, Mass of electrons : m = 9.11 × 10-28 g) %3D
- 9= 1. Photoelectric effect. In a photoelectric experiment in which monochromatic light of wave- length \ falls on a potassium surface, it is found that the stopping potential Vstop is 1.9 V for > 300 nm and 0.88 V for \ = 400 nm. Imagine we know neither Planck's constant, nor the workfunction for potassium, nor the threshold frequency fo. But assume we do know the elementary charge e 1.60 × 10-19 C and want to test the theoretical prediction of Eintsein's theory. = (a) From the given data, calculate a value for Planck's constant, h. (b) From the same data, find the workfunction Eo and the threshold frequency fo for potas- sium. (c) Then compare your results for h and Eo to their known values (see Knight, Table 38.1 for the work function). (d) Plot eVstop as a linear function of frequency f. Include the information you have found in parts (a) and (b) as well as the experimental data.A housing attached to a microprocessor uses radiator fins to get rid of excess heat. If the largest amount of radiation emitted by the fins has a frequency of 186.20 THz, what is the associated wavelength? m