The kinetic energy operator in 3-D is: a. Î= – Invalid element O b. O C. O d. T= ħ2² 2m - ·D2 ħ 2m ħ 2m V V
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a. Î= – Invalid <mfrac> element
O b.
O C.
O d.
T=
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2m
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- 4. What is the maximum acceleration potential (V) must be applied to electrons to cause electron diffraction on (220) planes of Lithium at 0 = 5°? (aLi = 3.517A°, m. = 9.1093837015 × 10' kg, q. = 1.6 × 10-19 coulomb, h = 6.62 x 10 34 J.S).c) The Bohr model of the atom postulated electrons orbiting around the nucleus in stable orbits. De Broglie explained what orbits could exist by postulating that electrons (and any- thing else) with momentum p have an associated wavelength λ, given by λ=h/p where h is Planck's constant. i) For an electron orbiting around a proton (the Bohr model), equating the centripetal force with the Coulomb force gives the expression v² = e²/(4πεmer). Calculate the speed of an electron orbiting at the Bohr radius, ˜Â = 0.053 nm. ii) Calculate the momenta and the de Broglie wavelengths of the electron of part (i) and of a bird (a racing pigeon) that weighs 0.350 kg and flies at 100 km per hour. iii) Compare the wavelength for the electron that you obtain in (ii) with the circumference of the orbit. Comment on this comparison. Explain briefly what it implies about the other possible orbits of the Bohr model and how the higher orbits might be predicted.What constraints does the uncertainty principle place on our knowledge of the world? To get a sense of scale, we’ll look at the uncertainty in speed for a confined electron and for a confined dust particle.a. What range of velocities might an electron have if confined toa 0.30-nm-wide region, about the size of an atom?b. A 1.0@mm@diameter dust particle (m ≈ 10-15 kg) is confined within a 5-μm-long box. Can we know with certainty if the particle is at rest? If not, within what range is its velocity likely to be found?
- The wavelength of the emitted photon from the hydrogen molecule H2 is 2.30 μm (micrometers) when the vibrational quantum number decreases by one. What is the effective "spring constant" for the H2 molecule in N/m ?What is the "zero point" energy (in eV) of the molecular vibration?Figure 1 of 1 > Energy (J) 4. 3. 2- 1- 1,2-1 +. -1 -21 K, + U, +Wt= K, + U, + AE %3D ext |||Which of the following principal levels contains / (angular momentum quantum number) = 3? A. n = 2 level B. both n = 3 and n = 4 levels C. n = 3 level D. n = 4 level How many orbitals are contained in the n = 3 principal number of a given atom? What is the value of the angular momentum quantum number of a d orbital?