With what speed would a rock of mass 49.0 g have to be thrown if it were to have a wavelength of 4.33 × 10¬34 m? Planck's constant is 6.63 × 10¬34 J . s. Answer in units of m/s.
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- The blackbody radiation emitted from a furnace peaks at a wavelength of 3.5 x 10-6 m (0.0000035 m). What is the temperature inside the furnace? K.When you talk about FM radio stations and talk about the frequency it emits at, you are talking about the frequency of the electromagnetic wave that leaves the station. Traditionally radio stations are measured in MHz, where 1MHz = 106 Hz. If a FM radio station is at 93.8 MHz, what is the energy in Joules of the photon associated with this radio wave? Planck's Constant is 6.63 x 10-34 J*sK 1...
- Imagine an alternate universe where the value of the Planck constant is ×6.62607·10−36Js . In that universe, which of the following objects would require quantum mechanics to describe, that is, would show both particle and wave properties? Which objects would act like everyday objects, and be adequately described by classical mechanics? object quantum or classical? A turtle with a mass of 560. g, 29. cm long, moving at 2.4 cm/s. classical quantum An iceberg with a mass of 3.8 x 108 kg, 80. m wide, moving at 0.75 km/h. classical quantum A mosquito with a mass of 1.2 mg, 11.4 mm long, moving at 2.5 m/s. quantum classical A buckyball with a mass of 1.2 x 10-21 g, 0.7 nm wide, moving at 40. m/s. classical quantumLight of frequency 2.1 × 1015 Hz illuminates a piece of cesium, and the cesium emits photoelectrons with a maximum kinetic energy of 6.5 eV. What is the threshold frequency of the metal? Planck’s constant is 6.63 × 10−34 J · s. Answer in units of Hz.The mass of an electron is 9.11 10-31 kg.A.) If the wavelength of an electron is 5.02 10-7 m, how fast is it moving? B.) If an electron has a speed equal to 4.30 106 m/s, what is its wavelength?
- Imagine an alternate universe where the value of the Planck constant is 6.62607x10−36J·s. In that universe, which of the following objects would require quantum mechanics to describe, that is, would show both particle and wave properties? Which objects would act like everyday objects, and be adequately described by classical mechanics? A mosquito with a mass of 1.1 mg, 8.7 mm long, moving at 2.7 m/s. A buckyball with a mass of 1.2 x 10-21 g, 0.7 nm wide, moving at 23. m/s. An iceberg with a mass of 3.4 x 108 kg, 160. m wide, moving at 1.21 km/h. An eyelash mite with a mass of 8.3 µg, 370 µm wide, moving at 27. µm/s.) a) What temperature is required for a black body spectrum to peak in the X-ray band? (Assume that E = 1 keV). What is the frequency and wavelength of a 1 keV photon? b) What is one example of an astrophysical phenomenon that emits black body radiation that peaks near 1 keV? c) What temperature is required for a black body spectrum to peak in the gamma-ray band with E = 1 GeV? What is the frequency and wavelength of a 1 GeV photon? d) What is one example of an astrophysical phenomenon that emits black body radiation that peaks at 1 GeV?A mosquito moving at 11 m/s has a de Brogliewavelength of 5.4 × 10−30 m.What is the mass of this mosquito?Planck’s constant is 6.63 × 10−34 J · s.Answer in units of kg.
- : 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. [The kilogram has been redefined based on Planck's constant (h) and a sphere of pure crystalline silicon: 8AsiVsphere Msphere = 2h 13 ст-а? The terms (with their relative uncertainties) are: (1) Planck's constant h (zero uncertainty as it is defined exactly); (2) the bracketed term including accurately known Rydberg constant R, speed of light c, mass of electron (me), and fine structure constant a, with a combined uncertainty of +4.7 × 10-8%; (3) atomic mass Asi for the 28 Si-enriched silicon (+5.4 x 10-7%); (4) volume of the Si sphere (+2.0 × 10-6%) and (5) crystal lattice parameter I (+1.84 x 10-7%). There are exactly eight atoms per unit cell in the sphere. Compute the relative uncertainty of myphere- To find the uncertainty of l, use the function y = x“, for which the uncertainty is propagated using %e, = a(%e,). relative uncertainty of msphere: % The mass of the sphere of pure silicon (999.698 336 5 g) must also be corrected for defects in the crystal lattice ( mdefects = 3.8…