Problem 1

Gold nanoparticles modified with two kinds of single-stranded nucleic acid fragments a and b aggregate in the presence of the target nucleic acid a'b' from the coronavirus, causing a colour change of the solution from red to blue within minutes. Gold nanoparticles are composed of closely packed gold atoms with the density of solid gold,

\rho = 19.3

g cm

^{-3}

. (a) Calculate the number of gold atoms

N

in a spherical gold nanoparticle of diameter 30.0 nm (

M(\ce{Au}) = 197.0

g mol

^{-1}

N_A = 6.022\times 10^{23}

mol

^{-1}

). (b) 5.2 mg of

\ce{HAuCl4*3H2O}

(

M = 394

g mol

^{-1}

) was completely converted into uniform spherical gold nanoparticles of diameter 30.0 nm in 100.0 mL of solution; the absorbance of the red solution measured at 530 nm in a 1 cm cuvette was 0.800. Calculate the molar extinction coefficient (per mole of nanoparticles) at 530 nm.

Step 3 of 3: Molar extinction coefficient

← Previous Next →

\varepsilon = \dfrac{A}{l\,c_{\text{NP}}} = \dfrac{0.800}{1\times 1.6\times 10^{-7}} = 5.0\times 10^{9}\ \text{L mol}^{-1}\text{cm}^{-1}

Analysis

Applying the Beer–Lambert law per mole of nanoparticles with $A = 0.800$ , $l = 1$ cm and $c_{\text{NP}} = 1.6\times 10^{-7}$ mol L $^{-1}$ gives $\varepsilon \approx 5.0\times 10^{9}$ L mol $^{-1}$ cm $^{-1}$ , the giant extinction that makes gold nanoparticles vivid colour reporters.