Ch. 43----Try: #2 (see example 43.1);  #6, #7, #9,( see example 43.3); #20, #21 (see example 43.8)

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SAMPLE EXAMS  #2
REAL EXAM 3
REAL EXAM 4
#2. (a) R = Ro*A1/3 .
Si: A = 28
Rb: A = 85
Tl:A = 205
(b) SURFACE AREA = 4*PI*R2. 
(c) VOLUME=(4/3)*PI*R3   .
(d) MASS DENSITY is approximately  (mP*A)/VOLUME,  where mP = proton (or neutron) mass. NOTE: All three nuclei have the same MASS DENSITY; SHOW THIS.
(e) NUCLEON DENSITY =A/VOLUME.  NOTE: SHOW this quantity is identical for all three elements. 
6. 

(a), (b):  

Note:  The mass defect and the binding energy E are flip sides of the same coin  since E = mc2, where  mass defect m = E/c2 .

There are nuances with textbook's equation 43.10:
E = (ZMH   + Nmn   - M)*c2. 
MH = mass of neutral  H atom, including electrons. M is the mass of atom also including the electrons. Clearly, 
ZMH -  M  cancels out the aggregate electron mass, leaving only   the difference between the sum of nucleon  masses (i.e., of protons and neutrons) and the mass of nucleus formed from  individual nucleons. 
NOTE:  MH = 1.007825 u, where u = 931.5 MeV/c2,   a quantity  including the proton and electron mass since we reference   neutral hydrogen. Also note:  Neutron mass mn  =    1.008665 u, nearly equal to the proton mass. 
By the way,  you may enjoy these links: 
 http://in.answers.yahoo.com/question/index?qid=20101019045512AADg9Qk
 or
 http://answers.yahoo.com/question/index?qid=20080512083456AAGa3Y9, 
though I cannot attest their  absolute accuracy; they only go to show mass defect is a hot topic!

In this problem,  M = 238.050783 u (the common isotope of uranium.) You can read  off A = 238 = Z + N and Z = 92. Thus N = 

238 - 92 = 146.  

(c) Compute E/A.  
 
7. hc/lambda = the binding energy =  (1*MH   + 1*mn   - M)*c2., where Table 43.2 lists M for Deuterium.  See also page 1474 for this computation and  numerical result. Find lambda. 
9. 
(a) hc/lambda  =  binding energy + kinetic energy =  (1*MH   + 1*mn   - M)*c2  +  kinetic energy. Find kinetic energy. 
(b) For both approximately equal masses,   sharing  energy democratically means (1/2)*mv2 = kinetic energy/2, where we got KE in  (a). 
20, 21. See examples 8, 9.  Take   steps to get  N = No*e -lambda*t :

20. (a) When a beta ray, nothing more than an electron,  shoots out of a nucleus, conservation of charge mandates  the new nucleus  becomes more positive by gaining a proton when a neutron converts into one,  increasing Z by one. New element has 38 + 1 since Z for Sr is 38. Note: A = 90 = Z + N remains the same but N decreases by one, offset by Z's increase. What's the new element? Consult a Periodic Table on or offline.
(b) 0.01 = e -lambda*t , after dividing out No*on both sides. Find t. Note you can get lambda from the given half-life. See SECTION 43.3.
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21. dN/dt = -lambda*  No *e -lambda*t  = -lambda*N , NOTE: N has a different meaning than  same symbol used in #20. 
Here N is the number of original nuclei remaining after decays.
 
0.350*3.70x1010 s-1  =  -lambda*N, where N can be found from the mass number and  sample's mass. One of the particles (nuclei) has mass of  124 u to a good  approximation; convert to kg and g. Divide into sample's  mass to get N.  Find lambda and then  the half-life.