Calculate the pressure in mm of mercury exerted by hydrogen if the number of molecules per cubic cm is 6.8*10^(15) and the root mean square speed of the molecules is 1.9*10^3 m/s
Comment on the effect of a pressure of this magnitude in a cathode tube.

I calculated the number of molecules per cubic meter is 6.8*10^(15)*1000000=6.8*10^(21)
then I used p=(1/3)nm<c^2>
where n is molecules per unit volume, <c^2> is the r.m.s. speed, and m is the mass of one molecule.
relative molecular mass of hydrogen is given as 2.02.
I plugged these values and got the pressure in Pa, then converted it to mmHg. Pa pressure=1.65*10^(28) and mmHg pressure then is 1.23*10^(26)
Answer is 0.21mmHg so my answer is way far off. where have i gone wrong?

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