The two strands of the helix-shaped DNA molecule are held together by electrostatic forces as shown in the Figure 16-44 in the textbook. 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^ - 10m.
a)
Estimate the net force between a thymine and an adenine. For each bond (red dots) consider only the three atoms in a line (two atoms on one molecule, one atom on the other). I got 4.6*10-10 N
b)Estimate the net force between a cytosine and a guanine.
7.1*10^-10 N
c)Estimate the total force for a DNA molecule containing 10^5 pairs of such molecules.
I don't understand this part I added and subtracted a from b but both answers were wrong please help me out thank you
I just had to look up the answer, as I couldn't figure it out either. Turns out it is rather simple. You need to add the two together and multiply by n=10^5, but only half of the bonds come from each type of base pair so you need to divide the final result by two to get the right answer. It asks for one sig fig, so it is 6X10^-5.
To estimate the total force for a DNA molecule containing 10^5 pairs of such molecules, you need to calculate the net force for each pair of molecules and then add them all up.
You have correctly calculated the net forces between a thymine and an adenine (4.6*10^-10 N) and between a cytosine and a guanine (7.1*10^-10 N).
To find the total force, you need to multiply each net force by the number of pairs of molecules. In this case, you have 10^5 pairs of molecules.
So, the total force is given by:
Total Force = (Force between a thymine and an adenine) * (Number of pairs) + (Force between a cytosine and a guanine) * (Number of pairs)
Plugging in the values, we get:
Total Force = (4.6*10^-10 N) * (10^5 pairs) + (7.1*10^-10 N) * (10^5 pairs)
To calculate the total force, we need to work with scientific notation. When multiplying numbers in scientific notation, you add the exponents:
Total Force = 4.6 * 10^-10 N * 10^5 pairs + 7.1 * 10^-10 N * 10^5 pairs
Total Force = (4.6 * 10^-10 N + 7.1 * 10^-10 N) * (10^5 pairs)
To simplify the calculation, you can add the coefficients:
Total Force = 11.7 * 10^-10 N * 10^5 pairs
Now, multiplying the numbers out:
Total Force = 1.17 * 10^-4 N * 10^5 pairs
Again, when multiplying numbers in scientific notation, you add the exponents:
Total Force = 1.17 * 10^(-4+5) N
Total Force = 1.17 * 10^1 N
So, the estimated total force for a DNA molecule containing 10^5 pairs of such molecules is approximately 11.7 N.
To estimate the total force for a DNA molecule containing 10^5 pairs of such molecules, you need to consider the forces between all the pairs and sum them up.
Let's calculate the force between one thymine and one adenine molecule (from part a):
Force between one pair = 4.6 * 10^-10 N
Now, since there are 10^5 pairs, we need to multiply the force by the number of pairs:
Total force for 10^5 pairs = (4.6 * 10^-10 N) * (10^5 pairs)
Calculating this, we get:
Total force for 10^5 pairs = 4.6 * (10^-10 N * 10^5 pairs)
Total force for 10^5 pairs = 4.6 * 10^-5 N
Therefore, the estimated total force for a DNA molecule containing 10^5 pairs of such molecules is 4.6 * 10^-5 N.