I have an idea about one formula : 381.51*4/Volume of unit cell, but i am not sure.
There are two main ways:
1. Based on unit cell
a) Determine the average size of AgNP using TEM image analysis
b) Find out the volume of one AgNP (assuming sphere shape) = V nm^3
c) You know the volume of unit cell (fcc) = 0.407^3 nm^3
d) Since one unit cell contains 4 Ag atoms (fcc), you can calculate number of atoms in one nanopartilce by:
V/(4x0.407^3)
2. Based on Avagadro's Number
a) You know the weight of silver taken for NP synthesis (Ag only, not silver salt) = W
b) Density of silver = 9.32 gcm-3
c) Now you calculate the volume of silver = W/9.320
d) Calculate the average size of nanoparticles using TEM (make sure nanoparticles are monodispersed) (2R)
e) Calculate the volume of a single nanoparticle (assuming sphere) = 4x(pi x R^3)/3 = V
f) You can calculate the number of particles in colloidal solution (N) = (W/9.32)/V
g) Calculate the weight of single AgNP = W/N or (9.32 x V)
h) Now use Avogadro’s number to get the number of Ag atoms in a single
NP.
No. Of atom /volume=1000*avogadro no.*density/atomic waight
Hear unit of volume & density is in S.I. Unit
Dear Shivani,
Please go through the file attached. I hope you can calculate the number of atoms in one particle.
There are two main ways:
1. Based on unit cell
a) Determine the average size of AgNP using TEM image analysis
b) Find out the volume of one AgNP (assuming sphere shape) = V nm^3
c) You know the volume of unit cell (fcc) = 0.407^3 nm^3
d) Since one unit cell contains 4 Ag atoms (fcc), you can calculate number of atoms in one nanopartilce by:
V/(4x0.407^3)
2. Based on Avagadro's Number
a) You know the weight of silver taken for NP synthesis (Ag only, not silver salt) = W
b) Density of silver = 9.32 gcm-3
c) Now you calculate the volume of silver = W/9.320
d) Calculate the average size of nanoparticles using TEM (make sure nanoparticles are monodispersed) (2R)
e) Calculate the volume of a single nanoparticle (assuming sphere) = 4x(pi x R^3)/3 = V
f) You can calculate the number of particles in colloidal solution (N) = (W/9.32)/V
g) Calculate the weight of single AgNP = W/N or (9.32 x V)
h) Now use Avogadro’s number to get the number of Ag atoms in a single
NP.
... the smaller the nanoparticle, the larger the possible error in calculation, just for possible surface reconstruction in case of ideal crystallinity of the particle. The methods above cited and based on the unit cell size provide a good approximation of the number of atoms as the nanoparticle size increases.
Sow, C. H., Udalagama, C. N. B., & Lim, G. Q. (2013). Teaching crystal structures using a transparent box with tennis balls. Journal of the NUS Teaching Academy, 3(1), 18-33.
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