16. || At what speed is an electron's de Broglie wavelength (a) 1.0 pm, (b) 1.0 nm, (c) 1.0 um, and (d) 1.0 mm?
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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).W | 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 +…3. Dimensional analysis can provide insight into Stefan-Boltzmann's law for the radiation from a black body. According to this law the intensity of radiation, in units of J s-' m-², from a body at temperature Tis 1 = GT*, where e is Stefan-Boltzmann's constant. Because black-body radiation can be considered to be a gas of photons, i.e. quantum particles which move with velocity e with typical energies of the order of kT, the intensity I is a function of h, c and kT. Use dimensional analysis to confirm that Iis proportional to 7 and find the dependence of a on h and c.
- 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.1.the electrons which are initially at rest are accelerated through a potential difference of 125V.calculate the de Broglie wavelength. 2.two long parallel wires carrying currents i1 and i2 in opposite directions. what are the magnitude and direction of the net magnetic field at point P ? ASSUME THE FOLLOWING VALUES i1=15A,i2=32A, and d=5.3cm.8. An electron is trapped within a sphere whose diameter is 5.20 x 10-15 m (about the size of the nucleus of a medium sized atom). What is the minimum uncertainty in the electron's momentum? kg.m/s
- 4. A laser with a power of 1.0 mW has a beam radius of 1.0 mm. What is the peak value of the electric field in that beam?a. 490 V/mb. 840 V/mc. 65 V/md. 120 V/me. 22 V/m3.1. What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of AV = 150 V?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
- 40. What must be the velocity, in meters per beam of electrons if they are to display a de Broglie wavelength of 850 nm? second, of aFigure 1 of 1 > Energy (J) 4. 3. 2- 1- 1,2-1 +. -1 -21 K, + U, +Wt= K, + U, + AE %3D ext |||ASS 3. When light with a wavelength of 222 nm is incident on a certain metal surface, electrons are ejected with a maximum kinetic energy of 3.16 × 10-¹⁹ J. Determine the wavelength of light that should be used to quadruple the maximum kinetic energy of the electrons ejected from this surface. nm fo 0 ssf60€ ssf606 5 09588 09 ssf60 ssf60