Description
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
(b) the escape speed from the Moon, 2.37 ✕ 103 m/s
K
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Explanation & Answer
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(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.
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