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.

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