The physics of the DNA molecule.
The two strands of the DNA molecule are held together by electrostatic forces. There are four bases which make up the DNA molecule, thymine (T), adenine (A), cytosine (C), and guanine (G). In two of the bases, thymine and adenine, an oxide ion with a single negative charge (O-) from the thymine base is attracted to a hydrogen ion (H+) from the adenine ion. The distance between the two ions is 28.0 nm. Note that the oxide ion
has a charge equivalent to a negative elementary charge and the hydrogen ion is equivalent to a positive elementary charge.
a) What is the strength of the electrostatic force between these two ions?
b) What is the direction of the force exerted on the oxide ion by the hydrogen ion?
(Assume that the oxide ion is to the right of the hydrogen ion.)
c) How many hydrogen ions would it take to equal the amount of charge contained in a lightning bolt, 25 coulombs?
To calculate the strength of the electrostatic force between the oxide ion (O-) and the hydrogen ion (H+), we can use Coulomb's law. Coulomb's law states that the electrostatic force between two charged particles is proportional to the product of their charges and inversely proportional to the square of the distance between them.
a) The formula for Coulomb's law is:
F = k * (q1 * q2) / r^2
where F is the electrostatic force, k is the electrostatic constant (approximately 9 × 10^9 Nm^2/C^2), q1 and q2 are the charges of the two particles, and r is the distance between the charges.
In this case, the charge of the oxide ion (O-) is -e (where e is the elementary charge) and the charge of the hydrogen ion (H+) is +e. The distance between the two ions is 28.0 nm, which is 28.0 × 10^-9 meters.
Substituting these values into the Coulomb's law equation, we get:
F = (9 × 10^9 Nm^2/C^2) * ((-e) * (+e)) / (28.0 × 10^-9 m)^2
Simplifying this expression, we find:
F = -e^2 * (9 × 10^9 Nm^2/C^2) / (28.0 × 10^-9 m)^2
This calculation will give us the absolute value of the force. The minus sign indicates the direction of the force, which we will determine in part (b).
b) The direction of the force exerted on the oxide ion by the hydrogen ion can be determined using Coulomb's law. Since the hydrogen ion carries a positive charge, the force exerted on the oxide ion will be towards the hydrogen ion. In this case, since the oxide ion is to the right of the hydrogen ion, the force will be directed towards the left.
c) To calculate the number of hydrogen ions required to equal the amount of charge contained in a lightning bolt (25 coulombs), we need to know the charge of a single hydrogen ion. The charge of a hydrogen ion is equal to the elementary charge, e.
So, we can divide the total charge of the lightning bolt (25 coulombs) by the charge of a single hydrogen ion (e) to find the number of hydrogen ions:
Number of hydrogen ions = 25 C / e
Note that 1 elementary charge is approximately equal to 1.6 × 10^-19 C.