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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- 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).The normalization PIB model with box size of 5.27 nm is constant (in SI units) for a O a. 23859 O b. 16871 O c. 19481 O d. 21780 O e. 13775W | File 70 Paste 14+1+13+1+12+|+11·10 ·9·1·8·1·7·1·6·1·5·1·4·1·3·1·2·1·1····1·1·20 Home Document1 - Microsoft Word (Product Activation Failed) Insert Page Layout References Review View T Calibri (Body) 14 T Α Α΄ B-B-S ## T AaBbCcDc AaBbCcDc AaBbC AaBbCc AaBl AaBbCcl BIU abe X, X² A ab T 트플 1 Normal No Spaci... Heading 1 Heading 2 Title Subtitle Font Paragraph G Styles ·2·1·1·····1·1·2·1·3·1·4·1·5·1· 6 · 1 · 7 · 1 · 8 · 1 ·9·1·10·1·11·1·12·1·13· |·14·1·15· |· · |·17· 1 · 18 · | I I I I I ATOMIC AND NUCLEAR PHYSICS PLEASE ANSWER ALL QUESTIONS The motion of two interacting particles (atoms or nuclei) can be described by the following radial Schrödigner equation d l(l 1) −2² [12 a (rªd) – (C,+¹) + V(r)]Re(k;r) = ERe(k;r). 2μ dr where Re(r) is the radial wave function, μ = 2, the reduced mass, V the interacting potential, my+m₂ E the total energy, and k the wave number, given by k = 2μE h² 2. Using Re(k,r) = u₂(k,r) kr show that the above Schrödigner equation reduces to l(l + 1)_24² ď² +…
- 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?a) Determine the quantum mechanical operators for the following: Lx = ypz - ZPy That is, find Îx = ŷpz - 2py where x = x êx = ħa i əx Ly = Zpx -xPz Ly = 2px - xpz ŷ = y Py = ћд і ду 2= Z Lz = xpy - ypx L₂ = xpy - ŷêx Pz = ћд і дz
- Chapter 4- questn-23 The position of an electron is given by i = 3.0tî – 4.0t2j + 2.0k , where r is in meter, t is in second. What is the angle between i and +x axis at t=2s. Option 1 Option 2 Option 3 Option 4 Option 5 78.4° 79.4° 80.4° 81.4° 82.4°Asap plzzzThe 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?
- A10. An acceptable wavefunction for the + equation is = Aeimo. What is the corresponding eigenvalue for the operator –ih if it is an eigenfunction of the operator? (a) imh (b) mħ (c) mh? (d) ħ A11. Which of the following represents the energy levels of a hydrogen atom? (a) The spacing between the energy levels decreases with increasing quantum number (b) The spacing between the energy levels increases with increasing quantum number (c) The spacing between the energy levels decreases with decreasing quantum number (d) The spacing between the energy levels is the same A12. Which of the following is the eigenfunction of the operator p, = -ih r ar %3D (a) eikr (b) reikr (d) sin(kr) A13. Which of the following correctly describes an electron in the hydrogen atom? (a) The wavefunction is described by the quantum numbers n p d (b) The wavefunction is described by the quantum numbers nI mi (c) The wavefunction is described by the quantum numbers nI ms (d) The wavefunction is described by the…M2False A Si photo-detector has a length of L= 10 um and a hole lifetime of t, =1x 10° s. If a voltage of 5 V is applied across the detector length, the detector gain "G" at the applied voltage will be: %3D Select one: O A. Gph = 2.925 B. Gph = 25.000 C. Gph = 4.000 %3! D. Gph = 10.000 %3D E. Gph = 1.250