At what temperature would the rms speed of neon-20 atoms equal the following spe

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At what temperature would the rms speed of neon-20 atoms equal the following speeds? (Note: The mass of a neon-20 atom is 3.32 ✕ 10−26 kg.)
(a) the escape speed from Earth, 1.12 ✕ 104 m/s 
 K 

(b) the escape speed from the Moon, 2.37 ✕ 103 m/s 

 K

Jun 19th, 2015

Thank you for the opportunity to help you with your question!

(k = Boltzmann constant 1.38x10^-23 J/(K.particle), T = Kelvin temp) 

From the kinetic theory .. mean particle KE (½mv²) = (3/2) kT 
mv² = 3kT 
T = mv² / 3k .. .. v = escape vel .. 

(a) For Earth .. 
T = 3.32x10^-26 kg x (1.12x10^4 m/s)² / (3 x 1.38x10^-23) .. .. ►T = 1.0x10^5 K 

(b) try now yourself, using the formula we derived. It will be helpful.

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 19th, 2015

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Jun 19th, 2015
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