Sphere Let us find the moment of inertia of a uniform solid sphere of radius a and mass m about an axis (the z-axis) passing through the center. We divide the sphere into thin circular discs, as shown in Figure 8.3.3. The moment of inertia of a representative disc of radius y, from Equation 8.3.7, isy²dm. But dm = pay² dz; hence, 2 4 8 I = py* dã = Enpa – z) dữ = pa 15 wa (8.3.8) The last step in Equation 8.3.8 should be filled in by the student. Because the mass m is given by we have m = na ³ p παρ I₂ = ² ma² for a solid uniform sphere. Clearly also, I₂ = ly = Iz (8.3.9) (8.3.10)

Let u,= 0.02 cm 1 and u, = 0.04 cm be the partial linear attenuation coefficients in the slab shown in the figure below. Let L = 5 cm and No = 106 particles. How many particles N, are transmitted, and how %3D many are absorbed by each interaction process in the slab? dt Uncharged partleles No N,

Please obtain the same result as in the book.

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H 1.

Find Ly, Ly Lz then estimated [12, Lx] when L= F xp (the angular momentum)

Legrende polynomials The amplitude of a stray wave is defined by: SO) =x (21+ 1) exp li8,] sen 8, P(cos 8). INO Here e is the scattering angle, / is the angular momentum and 6, is the phase shift produced by the central potential that performs the scattering. The total cross section is: Show that: 'É4+ 1)sen² 8, .

In spherical coordinates, the ladder operators for orbital angular momentum are of the form: Ĺ+ Ĺ a. b. C. = eip [Ĺ₂,Ĺ+] = ±Û± [L²,L+] = 0. [Ĺ+, Ĺ_] = 2Ĺ₂. e Cae Ә (- + icot 0. Ə 20 ə до 980) Show, by explicit calculation of the relevant products, that these operators satisfy the commutation relations +icot 0.

. Find Lande splitting factor g for neodymium using Hund Rule

2.