Question

A molecule of dna (deoxyribonucleic acid) is 2.23 µm long. the ends of the molecule become singly ionized: negative on one end, positive on the other. the helical molecule acts like a spring and compresses 1.13% upon becoming charged. determine the effective spring constant of the molecule.

Answer 1

end of the molecule become singly ionized mean charge on both the sides
Q = 1.6 * 10 ^ -19 C

F = KQ^2 / r^2
F = ( 8.99 * 10 ^-9 ) (1.6 * 10 ^-19) ^2 / (2.23 * 10 ^-6) ^2
F = 4.627 * 10^-17 N

F= Kx
x = 0.0113 ( 2.23 * 10^-6)

put values in F = Kx

4.627 * 10 ^-17 = K ( 0.0113 ( 2.23* 10 ^-6)
K = 4.627 * 10 ^ -17 / 2.519 * 10 ^ -8
K = 1.83c 10 ^-9 N/m