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TwopuTwo pure samples ofatoms, labeled A and B, contain oxygen atomsand carbon atoms,respectively. Each sample contains the same numberofatoms. What is the ratio of the mass of sample B to that ofsampleA, mB/mA? Notethe followingatomic masses: C = 12 u; O = 16 u.
(a)1.0 b).5 (c)2.0 d)1.5 (e)0.75
From the cannonical commutation relations [xl,pm]=i(hbar)δlm (l,m = 1,2,3 or x,y,z) and thefact that the orbital angular momentum operator is defined L=r x p,prove the following commutation relations.(a) [Lx,Ly]=i(hbar)Lz(b)[L2,Lx]=[L2,Ly]=[L2,Lz]=0,whereL2=Lx2+Ly2+Lz2(c) [L2, L±]=0 (L± =Lx ± iLy)
(d) [L± , Lz] = (-/+)(hbar)L±
(e) [L+, L-] = 2(hbar)Lz
Hint: Just use Commutator Algebra Rules [A,B]=-[B,A] and [AB,C]= A[B,C] + [A,C]B
Thin lenses. Object O stands on the central axis of a thinsymmetric lens. For this situation, each problem in Table 34-6(below) gives object distance p (centimeters), the type of lens (Cstands for converging and D for diverging), and then the distance(centimeters, without proper sign) between a focal point and thelens. Find (a) the image distance i and (b) the lateralmagnification m of the object, including signs. Also, determinewhether the image is (c) real (enter 1) or virtual (enter 0), (d)inverted (enter 1) from object O or noninverted (enter 0), and (e)on the same side of the lens as object O (enter 1) or on theopposite side (enter 0).p Lens (a) i (b) m (c) R/V (d) I/NI (e) Side50 +13 D, 8.751 +8.0 D, 1252 +16 C, 4.053 +12 C, 1654 +12 D, 3155 +45 C, 2056 +25 C, 3557 +22 D,14
