a thermal neutron has a speed v at temperature T=300K and kinetic energy m0v^2/2=3kT/2.calculate its de Broglie wavelength .state whether a beam of these neutrons could be diffracted by a crystal and wh
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a thermal neutron has a speed v at temperature T=300K and kinetic energy m0v^2/2=3kT/2.calculate its de Broglie wavelength .state whether a beam of these neutrons could be diffracted by a crystal and why?
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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?Suppose a star with radius 8.57 × 108 m has a peak wavelength of 680 nm in the spectrum of its emitted radiation. (a) Find the energy of a photon with this wavelength. J/photon (b) What is the surface temperature of the star? K (c) At what rate is energy emitted from the star in the form of radiation? Assume the star is a blackbody (e = 1). W (d) Using the answer to part (a), estimate the rate at which photons leave the surface of the star. photons/sCalculate the de Broglie wavelength (in fm) of a 5.8 MeV a particle emitted from an atomic nucleus whose diameter is approximately 1.6 × 10¯14, fm Calculate its minimum kinetic energy (in keV) according to the uncertainty principle. keV Could this particle exist inside the nucleus? Yes No Explain. m.
- A hydrogen atom is initially in the n = 6 state. It drops to the n = 2 state, emitting a photon in the process. (a) What is the energy (in ev) of the emitted photon? Enter a number. ergy of a hydrogen atom related to the quantum number n? What is the atom's initial energy? Its final energy? From these values and conservation of energy, what is the photon's energy? ev (b) What is the frequency (in Hz) of the emitted photon? Hz (c) What is the wavelength (in um) of the emitted photon? umFor 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?3.1. What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of AV = 150 V?
- 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?An x-ray is modeled by the equation E= (1000V/m)sin(kx - 8.96 *1018t) What is the wavenumber, k, in m-1, of this x-ray?