Solution :
According to the Graham's law of diffusion, we know that, the rate of the diffusion varies inversely to the molar mass of the gas, i.e.
Rate of diffusion, [tex]$r_d = \frac{a}{\sqrt M}$[/tex]
where, the 'M' is the molar mass of the gas.
Now in the case of the isotopes of the Krypton,
Atomic mass of [tex]$^{80}Kr$[/tex] = 80 AMU
Atomic mass of [tex]$^{82}Kr$[/tex] = 82 AMU
Atomic mass of [tex]$^{83}Kr$[/tex] = 83 AMU
So the ratio of the rate of diffusion of the three isotopes are :
[tex]$M_{d,^{80}Kr}:M_{d,^{82}Kr}:M_{d,^{83}Kr}$[/tex]
[tex]$=\frac{1}{\sqrt{80}}:\frac{1}{\sqrt{82}}:\frac{1}{\sqrt{83}}$[/tex]
[tex]$=0.1118:0.1104:0.10976$[/tex]
Dividing the above three with the smallest number among the three i.e. 0.10976, we get the relative rates of diffusion.
∴ [tex]$M_{d,^{80}Kr}:M_{d,^{82}Kr}:M_{d,^{83}Kr}$[/tex]
= 1.02 : 1.01 : 1
Hence the relative rate of diffusion are :
[tex]$^{80}Kr(1.02)>^{82}Kr(1.01)>^{83}Kr(1.00)$[/tex]
