Question

A molecule of DNA (deoxyribonucleic acid) is 2.31

Answer 1

  Since one end of the DNA is negatively charged by a single electron, and the other end is positively charged, then the two ends attract each other.

You know the distance between the two charges, so you can compute the attractive force between them.

Also DNA acts like a spring that opposes being compressed.

Once the DNA is compressed to .96% of its original length, the the electrical force of attraction between the ends must be equal to the opposing spring force of the DNA.

Use the formula for computing the attractive electrical force:

F_e = (K * q1 * q2 ) / (d^2) using the distance d=(.0096)*(.00000231 m )

=2.2e-8m

(remember that this must be in meters)

And use the spring equation: F_s = k * x , where k is the spring constant, and x is the amount of compression from equilibrium:

x=(original length) -(final length)
x = (0.00000231 m ) - ( .0096 )*( 0.00000231 m )

x= 231e-8 -2.2e-8m

x=228.8e-8m

Set the two force equations equal to each other , and solve for k

(K * q1 * q2 ) / (d^2)=k * x

9*10^8/(2.2e-8m)^2=k*228.8e-8m

1.8e24/228.8e-8m=k

0.00812e32=k