The Maxwell\'s speed distribution Consider helium gas under normal conditions (T

Question

The Maxwell's speed distribution Consider helium gas under normal conditions (T=300K). speeds V_1 is chosen so that the average number of particles with speeds larger than V_1 is 25% of the total number of particles in the gas. Find V_1. You do not have to write a squareroot solver for this. Full credit will be given if you present a clear formula (equation) for which the speed you are looking for is a solution, and estimate the answer by any means of your choice. In the end, the equation needs to be in the form of an integral of a non-dimensional variable and contain V_1. An easy way to the answer then would be to plot the equation using a computer and find the answer graphically. The printout of the plot (or any material related if you choose to proceed otherwise) needs to be included in the submitted work

Explanation / Answer

v = sqrt(3RT/mN)

where m is the mass and N is the avogadro's num

now v is chosen such that the average number of particles with speeds larger than v is 25% of the total number of particles in gas = 25/100 * N = 0.25 * 6.023*1023

so, v = sqrt [(3 * 8.314 *300)/( 6.6*10-27*0.25 * 6.023*1023)]

v =2744.6m/s

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