User:Allison K. Alix/Notebook/Thesis Research/2013/06/12

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(Calculating AuNP concentration in g/L)
(Calculating AuNP concentration in g/L)
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==Calculating AuNP concentration in g/L==
==Calculating AuNP concentration in g/L==
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''1) Calculate the volume of 1 AuNP''
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1) Calculate the volume of 1 AuNP
Volume of 1 AuNP = 4/3πr<sup>3</sup>, where r = d/2 = 19.25nm
Volume of 1 AuNP = 4/3πr<sup>3</sup>, where r = d/2 = 19.25nm
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'''V= 2.988x10<sup>17</sup>cm<sup>3</sup>'''
'''V= 2.988x10<sup>17</sup>cm<sup>3</sup>'''
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''2) Calculate the mass of 1 AuNP''
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2) Calculate the mass of 1 AuNP
density of Au = 19.3g/cm<sup>3</sup>
density of Au = 19.3g/cm<sup>3</sup>
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19.3g/cm<sup>3</sup> x 2.988x10<sup>17</sup>cm<sup>3</sup> = '''5.7668x10<sup>-16</sup> g per 1 AuNP'''
19.3g/cm<sup>3</sup> x 2.988x10<sup>17</sup>cm<sup>3</sup> = '''5.7668x10<sup>-16</sup> g per 1 AuNP'''
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''3) Calculate # of AuNP in 20mL solution''
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3) Calculate # of AuNP in 20mL solution
0.43x10<sup>-9</sup>mol/L x 20mL x 1L/1000mL x 6.02x10<sup>23</sup>AuNP/1 mol = '''5.219x10<sup>12</sup> AuNP'''
0.43x10<sup>-9</sup>mol/L x 20mL x 1L/1000mL x 6.02x10<sup>23</sup>AuNP/1 mol = '''5.219x10<sup>12</sup> AuNP'''
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4) Calculate mass of all AuNP in 20mL solution
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5.7668x10<sup>-16</sup> g/1 AuNP x 5.219x10<sup>12</sup>AuNP x 1/20mL x 1000mL/1L = 0.1505g/L
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Revision as of 13:01, 12 June 2013

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AuNP synthesis

Note: These AuNPs will be used in the silica coating procedure. See calculations below.

Calculating AuNP diameter and concentration

λspr= 527nm

d= [ln(λspr0/L1)]/L2

where λ0= 512nm, L1= 6.53, and L2=0.0216 (These are fit parameters from theoretical calculations1)

d= [ln(527nm-512nm/6.53)]/0.0216

d= 38.5nm

c = A450450

c = 1.89/(4.36x109)

c = 0.43nM

Calculating AuNP concentration in g/L

1) Calculate the volume of 1 AuNP

Volume of 1 AuNP = 4/3πr3, where r = d/2 = 19.25nm

V= 4/3π(19.25x10-9m)3

V= 2.988x1023m3

V= 2.988x1017cm3

2) Calculate the mass of 1 AuNP

density of Au = 19.3g/cm3

19.3g/cm3 x 2.988x1017cm3 = 5.7668x10-16 g per 1 AuNP

3) Calculate # of AuNP in 20mL solution

0.43x10-9mol/L x 20mL x 1L/1000mL x 6.02x1023AuNP/1 mol = 5.219x1012 AuNP

4) Calculate mass of all AuNP in 20mL solution

5.7668x10-16 g/1 AuNP x 5.219x1012AuNP x 1/20mL x 1000mL/1L = 0.1505g/L



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