integral (-inf to inf) [e^(-x^2/2 sigma^2) dx / sqrt(2*pi*sigma^2)] = 1
=> integral (-inf to inf) [e^(-x^2/2 sigma^2) dx] = sqrt(2*pi*sigma^2)
=>integral (0 to inf) [e^(-x^2/2 sigma^2) dx] = sqrt(2*pi*sigma^2)/2
=> integral (0 to inf) [e^(-c*x^2) dx] = sqrt(pi/c)/2

Because, probability function,
f(x) ...

Solution Summary

The solution discusses (Ross # 5.1 - Theoretical) The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by ....

... rms speed is a good approximation of the the typical speed of the molecules in a gas. This histogram shows a theoretical distribution of speeds of molecules in ...

Speed of Reaction vs Number of Collisions Required. ... whether reactions requiring less molecular collisions are ... well as how a pressure cooker speeds cooking times ...

... A) higher temperatures slow down the speed of the molecules B) molecular collisions are elastic C) ideal gas molecules travel in a straight line D) the ...

... Number of up down (or to and fro) cycles completed by each molecule is known as the frequency of the wave ...Speed = Wave length x Frequency = 0.65 x 500 = 325 m/s. ...

... The average speed of nitrogen molecule in air is about 6.70x10^2m/s, and its mass is 4.68x10^(-26) kg a) If it takes 3.00x10^-13s for a nitrogen molecule to ...

... of time until it gives its energy to a nearby molecule. ... partly propagates into the brick with higher speed than it ... As we said in I, the angular speeds are the ...

...Molecules with different speeds would hit the disk at ... of a material that will cause the molecules hitting it ... the disk one can then deduce the speed distribution ...