A molecule consists of two atoms. The atoms have masses of 21 u and 17 u and are 1.63 10-10 m apart. How far from the first atom is the center of mass of the molecule?
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2007-03-21 05:24:27 · 2 answers · asked by Foxx 1 in Science & Mathematics ➔ Physics
The concept of centre of mass takes into account taking moments of masses about CM.
The position of center of mass is given by
r = [m1 r1+ m2 r2] / (m1+m2)
where distances are from origin at the left side in such a way that r1 > r and r < r2
required distance = r - r1 = [m1 r1+ m2 r2 / (m1+m2)] - r1
L = [m1 r1+ m2 r2 - m1 r1 - m2 r1] / (m1+m2)
L = m2 [r2 - r1] / (m1+m2)
r2 -r1 = 1.63 * 10^-10 and m2/(m1+m2) = 17 / 38
L = 1.63 * 10^-10 (17 / 38) = 0.729 *10^-10
L= 0.729 Angstrom
2007-03-21 06:49:58 · answer #1 · answered by anil bakshi 7 · 0⤊ 0⤋
It's no different than a teeter-totter. Assume the first atom is at point 0 and the second atom is at point 1.63 along a line. The center of mass is 17/(17+21) of the way from the more massive molecule to the less massive molecule. I'll leave to you the arithmetic to multiply this fraction by 1.63 to get the actual distance.
2007-03-21 05:59:20 · answer #2 · answered by Isaac Laquedem 4 · 0⤊ 1⤋