An uncharged molecule of DNA (deoxyribonucleic
acid) is 2.17 µm long. The ends
of the molecule become singly ionized so that
there is a charge of −1.6 × 10−19 C on one end
and +1.6 × 10−19 C on the other. The helical
molecule acts like a spring and compresses
1.3% upon becoming charged.
Find the effective spring constant of the
molecule. The value of Coulomb’s constant is
8.98755 × 109 N · m^2
e = 1.6x10^-19 C
F = kQ²/r² F = (8.98755x10^9)(1.6x10^-19)²/(2.17x10^-6)² F = 4.886x10^-17 N F = Kx x = 0.0108(2.17x10^-6) 4.886x10^-17 = K(0.0108(2.7x10^-6) K = 2.085c10^-9 N/m
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