Nanoparticles with a gold core and organothiol outer shell with well-defined stoichiometries Aux(SR)yAu_x(SR)_y i can be prepared and isolated.

a. The MALDI-time-of-flight mass spectrum of the nanoparticle with R=CH2CH2C6H5 R=CH₂CH₂C₆H₅ exhibits a  broad molecular ion at m/z 76.3 kDa. m/z 76.3 kDa. Electrospray ionization gives a series of sharp peaks at  m/z 38 152.7 m/z 38 152.7 (charge=+2),(charge =+2), 25 433.3 (+3),25 433.3 (+3), 19 075.2 (+4),19 075.2 (+4), and  15 260.4 (+5). 15 260.4 (+5). Find the average molecular mass of Aux(SCH2CH2C6H5)y Au_x(SCH₂CH₂C₆H₅)_y from  the four peaks.

b. In another electrospray experiment, the (z=-3) (z=-3) ions for three different thiol shells were found at  m/z 27 243 (R=n-C12H25), m/z 27 243 (R=n-C₁₂H₂₅) 25 440 25 440(R=CH2CH2C6H5),(R=CH₂CH₂C₆H₅), and  24 8762 24 8762 (R=n-C6H13).(R=n-C₆H₁₃)Compute the mass of the molecular ion for the three Aux(SR)y Au_x(SR)_y nanoparticles. Assuming that x^x is constant, find the value of y^y for each nanoparticle from the difference in  molecular mass between the molecular ions. From the value of y^y find the value of x^x. Note that AuAu is  monoisotopic with a mass of 196.966 6.196.966 6.

2 nm -Thiol shell (-SR) R=n-CH25, n-C6H13 CHCHCH5 -Au core