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?

 

[paranormal]

The net force in a DNA molecule is the result of the electrostatic forces between the atoms. These forces are caused by the difference in charge between the atoms. In this case, we can estimate the net force between different pairs of atoms in a DNA molecule using Coulomb's law, F=k(q1q2)/d^2.

For the first bond, between thymine and adenine, we can calculate the net force by considering the three atoms in a line. Using the given net average charges of 0.2e and 0.4e for H/N and C/O atoms respectively, and a distance of 1.0E-10 m between the atoms, we can calculate the net force to be approximately 1.79E-8 N.

For the second bond, between cytosine and guanine, we can use the same equation to calculate the net force. In this case, the net force is approximately 3.57E-8 N.

To estimate the total force for a DNA molecule containing 105 pairs of such molecules, we can simply multiply the net force for each bond by 105. This gives us a total force of approximately 1.88E-6 N.

In conclusion, the net force in a DNA molecule is due to the electrostatic forces between the atoms, and can be calculated using Coulomb's law.