Electric Forces and Electric Fields

[Dita]

I need help with the following, I don’t even know how to start

A molecule of DNA ( deoxyribonucleic acid) is 2.17μm long. The ends of the molecule become singly ionized – negative on one end, positive on the other. The helical molecule acts as a spring and compresses 1.00 % on becoming charged. Determine the effective spring constant of the molecule.

[Chen]

Maybe you're having problems with "singly ionized"? It means that each side of the molecule is charged with by one elementary charge. That is obviously the charge of the electron/proton, so you can just say that one side gains an electron while the other side loses one. Because of this there is an electric force between the two sides of the molecule, which is equal to:

F_{ele} = K\frac{q_e^2}{d^2}

Where d is the distance between the charges, in our case 2.17μm. That is the force that causes the spring-like molecule to compress. Now you can use Hooke's law (http://hyperphysics.phy-astr.gsu.edu/hbase/permot2.html#c3) to find the spring's constant, since you know the magnitude of the force as well as the compression length (1% of 2.17μm). The answer should be 2.45x10-9 N/m.