What Determines the Net Force in a DNA Molecule?

[treedwellerjess]

Net Force in a DNA molecule??

Homework Statement

The two strands of the helix-shaped DNA molecule are held together by electrostatic forces as shown in Fig. 16-44. Assume that the net average charge (due to electron sharing) indicated on H and N atoms is 0.2e and on the indicated C and O atoms is 0.4e. Assume also that atoms on each molecule are separated by 1.0 10-10 m


Estimate the net force between each of the following. For each bond (red dots consider only the three atoms in a line (two atoms on one molecule, one atom on the other)).
(a) a thymine and an adenine

(b) a cytosine and a guanine

(c) Estimate the total force for a DNA molecule containing 105 pairs of such molecules.

Homework Equations

F=k (q(1)q(2))/d^2 k=8.99E-9

The Attempt at a Solution

 

[Warr]

You have to post what you have tried first

 

[dsoltyka]

I am trying to solve this same problem.

The two strands of the helix-shaped DNA molecule are held together by electrostatic forces as shown in figure 16-44. Assume that the net average charge (due to electron sharing) indicated on H and N atoms is 0.2e and on the indicated C and O atoms is 0.4e. Assume also that the atoms on each molecule are separated by 1.0 * 10^-10 m. Estimate the net force between a) a thymine and an adenine; b) a cytosine and a guanine. For each bond (red dots) consider only the three atoms in a line (two atoms on one molecule, one atom on another). c) Estimate the total force for a DNA molecule containing 10^5 pairs of such molecules.

Basically I started with (a) which was finding the force between thymine and adenine. They share an O-H-N bond (O being on the Thymine molecule, H and N being on the Adenine molecule) and a N-H-N bond (N and H on the Thymine, N being on the Adenine)

This question has had me sort of stumped for some time now. I've worked out what I thought was the solution, however I was incorrect. Here's what I thought was correct.

O-H-N bond

O and N are negative, H is positive

O...H---------N

Using our reading, I assumed I should consider them Q1 through Q3, each separated by r.

So we'd have:

Q1...Q2--------Q3

Since the bond (red dots) are between Q1 and Q2/Q3, I assumed I should find the net force on Q1

F12 = k[(Q1)(Q2)]/r^2 , where Q1 = .4e, Q2 = .2e, and r = 1.0 * 10^-10

Solving the equation I have F12 = 1.8432 * 10^-9 N

The same is then done for F13 (except that r = 2.0 * 10^10) , solving the equation I get F13 = 4.608 * 10^-10

As F12 is attractive and F13 is repulsive, I added the forces

F = 1.8432 * 10^-19 + (-4.608 * 10^-10) = 1.3824 * 10^-9

I did the exact same thing for the N----H...N bond as well (N being negative, H being positive), but for this I calculated the forces being applied to Q3 instead of Q1

The results where

F = 6.912 * 10^-10I then added the forces, as one of each bond exists between T & A, and was left with 2.0736 * 10^-10, which is unfortunately incorrect. The book shows the answer as being 4.6 * 10^-10.I understand this will be difficult to decipher without having the textbook figure. Attached is a picture of the figure from the text, I hope it helps.

 

[Quantum Shadd]

What textbook are/were you using for this problem?