If $r$ is the radius of the atom then the volume of each atom will be $(4 / 3) \pi r^{3}$ Volume of all the substance will be $=(4 / 3) \pi r^{3} \times N=M / \rho$ $M=$ atomic mass of the substance...
Given below are densities of some solids and liquids. Give rough estimates of the size of their atoms:
[Hint: Assume the atoms to be ‘tightly packed’ in a solid or liquid phase, and use the known value of Avogadro’s number. You should, however, not take the actual numbers you obtain for various atomic sizes too literally. Because of the crudeness of the tight packing approximation, the results only indicate that atomic sizes are in the range of a few ![\AA]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9adcf51f181c503063a9896541caf3e4_l3.png "Rendered by QuickLaTeX.com")
.
read more
![\mathbf{n}_{2}=\mathbf{n}_{1} \exp \left[-m g\left(h_{2}-h_{1}\right) / k_{B} T\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-5b5b6d5115539a7874b2e10ab623c3f2_l3.png "Rendered by QuickLaTeX.com")
refer to number density at heights 
and 
respectively. Use this relation to derive the equation for sedimentation equilibrium of a suspension in a liquid column: ![n_{2}=n_{1} \exp \left[-m g N_{A}\left(\rho-\rho^{\prime}\right)\left(h_{2}-h_{1}\right) /(\rho R T)\right]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3ff42d2faa5d415ef6a8e9eb3c38ae70_l3.png "Rendered by QuickLaTeX.com")
is the density of the suspended particle, and 
is Avogadro’s number, and 
the universal gas constant.] [Hint: Use Archimedes principle to find the apparent weight of the suspended particle.]
1. The diffusion of another gas under the same conditions is measured to have an average rate of 
. Identify the gas.
, where 
are diffusion rates of gases 1 and 2 , and 
and 
their respective molecular masses. The law is a simple consequence of kinetic theory.]
long mercury thread, which traps a 
column of air. What happens if the tube is held vertically with the open end at the bottom?
atm and temperature 
. Take the radius of a nitrogen molecule to be roughly 
A. Compare the collision time with the time the molecule moves freely between two successive collisions (Molecular mass of 
).
(atomic mass of 
, of 
).
the largest?
,
at a temperature of 
and 1 atm pressure.
rises from the bottom of a lake 
deep at a temperature of 
To what volume does it grow when it reaches the surface, which is at a temperature of 35 C?
After some oxygen is withdrawn from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to 
, molecular mass of 
.
for 
of oxygen gas at two different temperatures.
Show that it is 
litres.