Show that the form factor for the charge distribution of model I for a nucleus of radius a is F(q²) = 3{sin(ga/h)–(qa/ħ)cos(qa/ħ)} (qa/ħ)*
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- (2) Stirling's formula is given by the following, depending on the accuracy you need:* In N! N In N - N or, +즐 In N! ≈ N ln N − N + √ln(2´N) Evaluate the accuracy of these formulas for N = 5, 10, 20, 60. Is it reasonable to expect the same accuracy for both formulas at very large N? *(Aside: Actual Stirling's formula is for gamma function П(z) ≈ FO where z is a complex number, and П(n + 1) = n! for nЄ N.)Please answer within 90 minutes.Problem 7: Consider what you've learned so far regarding the nucleus of an atom.
- Find v* for N2 gas in air (a) on a cold day at T = 15°C and (b) on a hot day at T = 35°C.By using the principle of accuracy, he proved the impossibility of the electron being inside the nucleus, given that the radius of the nucleus is 1 x 10-14m.Use the semiempirical mass equation to compute, for given A, the relation between Z and N for a nucleus that has Sn 4 0 (the neutron "drip line"). Compute N/Z for A 4 100.
- Alpha particles of energy 8.4 MeV are incident on a silver foil of thickness 6.5 μm. For a certain value of theimpact parameter, the alpha particles lose exactly half their incident kinetic energy when they reach theirminimum separation from the nucleus. Find the minimum separation, the impact parameter, and the scatteringangle.In a Rutherford scattering experiment, an a-particle (charge = +2e) heads directly toward a gold nucleus (charge = +79e). The α-particle had a kinetic energy of 5.0 MeV when very far (r→ ∞) from the nucleus. Assuming the gold nucleus to be fixed in space, determine the distance of closest approach. Hint: Use conservation of energy with PE =kq1q2/r.Calculate the standard uncertainty in z if z=Xsinθ using the angle (57.00 +- 0.85) degrees and the value X = (58.20 +- 0.77)
- Is this the correct way to solve for W(ca)In a scattering experiment, an alpha particle A is projected with the velocity up = -(600 m/s)i + (750 m/s)j - (800 m/s)k into a stream of oxygen nuclei moving with a common velocity vo = (630 m/s)j. After colliding successively with nuclei B and C, particle A is observed to move along the path defined by the Points A₁(280, 240, 120) and A2(360, 320, 160), while nuclei B and Care observed to move along paths defined, respectively, by B₁(147, 220, 130), B2(114, 290, 120), and by C₁(240, 232, 90) and C₂(240, 280, 75). All paths are along straight lines and all coordinates are expressed in millimeters. Knowing that the mass of an oxygen nucleus is four times that of an alpha particle, determine the speed of each of the three particles after the collisions. The speed of particle A is The speed of particle B is The speed of particle Cis m/s. m/s. m/s.A certain atom has 76 protons. Assume that the nucleus is a sphere with radius 6.63 fm and with the charge of the protons uniformly spread through the sphere. At the nucleus surface what are (a) the magnitude and (b) direction (radially inward or outward) of the electric field produced by the protons? Units (a) Number (b)