00:02
Dear students, in the question, gold nanoparticle, diameter of each particle is 2 nanometer and density is 19 .3 gram per ml.
00:11
1 amu in gram is also given.
00:14
We have to calculate number of particles in one, number of atoms in one nanopatical of gold.
00:21
Now let us find out the volume of each nanoparticle, volume of each particle, equal to we know 4 by 3, considering at a spherical, 4 by 3 pi r q, where r is the radius.
00:41
4 by 3 .14 multiplied by r is radius.
00:50
So here 2 nanometer equal to 2 multiplied by 10 to the power minus 9 meter or minus 7 centimeter.
01:02
Because here density is given in ml so let us take in centimeter here this is not a liquid so it is not possible in ml so it is cc cm cc or cm cube so this is a gram per cmq so let us take it in centimeter so it is 2 multiplied by tensor minus 7 centimeter so 2 multiplied by 100 minus 7 divided by 2 because it is radius so it is half of the diameter which is equal to here 2 -2 cancels out now 4 multiplied by 3 .14 multiplied by 10 to the power 21 minus 21 divided by 3 which is equal to it is nearly 4 .2 multiplied by 10 to 1 cm cube.
02:01
So this is the volume.
02:03
Now let us find the mass of each particle.
02:08
Mass of each particle is density volume by a density divided by volume...