Energy of DNA base pairing, II. (See Problem 25 in Chapter 17 ; see also Figure 17.44 . ) Calcul

Energy of DNA base pairing, II. (See Problem 25 in Chapter...

Key Concepts

Electric Potential Energy

This is the energy stored in a system due to the positions of charged particles, typically calculated using Coulomb’s law. It represents the work required to assemble a system of charges by bringing them from infinity to a finite separation, and it plays a crucial role in understanding intermolecular interactions.

Coulomb’s Law

Coulomb’s law quantifies the force between two point charges and is fundamental for calculating electric potential energy in a system. It describes how the force between charges is inversely proportional to the square of the distance between them, which in turn allows one to calculate the energy associated with different charge configurations and distances.

Hydrogen Bonding

Hydrogen bonds are specific non-covalent interactions where a hydrogen atom, covalently bonded to an electronegative atom, interacts with another electronegative atom in a nearby molecule. This type of bonding is critical in many biological molecules, as it stabilizes complex structures like those found in DNA through directional and distance-dependent interactions.

DNA Base Pairing

DNA base pairing involves specific interactions between nucleotide bases that stabilize the double helix structure of DNA. In particular, guanine and cytosine form a set of hydrogen bonds, contributing to the overall stability and fidelity of the genetic material. Understanding the electrostatic contributions of these bonds helps elucidate the nature of molecular recognition in biological systems.

Transcript

00:01 In this question, we are given a dna -based pairing, and we want to calculate the electric potential energy of this bond with using the same combination of different molecules.

00:15 And at the same time, we also want to compare this bonding energy with the potential energy of the proton -electron pair in the hydrogen atom.

00:25 So there are, this question asks us to refer to problem 24 in chapter 7.

00:30 Which further refers to some other numbers.

00:33 So at first i just want to write down all the numbers that this question expect the reader to already know.

00:41 So in the oxygen -hydrogen - nitrogen bond, the oxygen iron and the hydrogen arrow is 0 .170 nanometer.

00:55 And the oxygen iron and the nitrogen iron and the nitrogen.

01:01 Iron, these are 0 .280 nanometers.

01:07 This is one you can read from the graph.

01:11 And for the nh in font, the nitrogen is 0 .190 nanometer from the hydrogen, and the whole thing is 0 .30 nanometer.

01:29 So these are distances that was given to you in in chapter 17 in the question that this question is referring to.

01:39 And for part b, this is for part a, for part b, we also need to know that in the hydrogen atom, the electron and proton are 0 .05 to 9 nanometer apart.

01:53 Okay, so you cannot finish this question without knowing these numbers.

01:59 Now let's get started.

02:01 In part a, it asks us to find the electric potential energy of both, both these bonds.

02:08 And the potential energy of a single iron here because due to the other iron can be found by the formula u equals k q q prime over r.

02:20 So for the oh n bound we have two different things going on.

02:25 We have oxygen with hydrogen and oxygen with nitrogen.

02:30 So the potential energy is also the addition of the two.

02:36 So potential energy equals q of oxygen iron over, so actually i will write them separately, oxygen iron types.

02:51 The first one is the q of hydrogen iron over radius of oxygen and hydrogen, plus the second one is q of nitrogen iron.

03:05 All of them carry a charge of one electron, so it's always one point.

03:09 It's always 1 .6 times 10 to the negative 19 over r over oxygen and nitrogen.

03:20 So this is k equals.

03:28 So firstly, this one is negative.

03:30 So negative 9 times 10 to the 9 times the oxygen is 1 .6 times 10 to 0 .6 times 10 to 0 .6 .5 times 10 to negative 13.

03:58 Okay, so this is squared and times.

04:07 So this is both this and this.

04:10 Because they all carry one electrons, so both of them are 1 .6 times 10 to the negative 19.

04:17 Then we have distance 1 over 0 .17 times 10 to the negative time meters.

04:28 And minus, because nitrogen iron is a negative number, minus 1 over 0 .28 times 10 to the negative die.

04:42 Okay, so we calculate it and we get...

04:50 Oh, so if we calculate it, we find that one of them, they're not in the same order of magnitude, one is actually significant.

05:05 Larger than the other.

05:07 So if we do the calculation, what we find is that the final answer is negative 0 .528 times 10 to the negative 18 gel or can write it is 5 .28 times 10 to the negative 18 jaw.

05:39 Okay, so that is for the oh, hn.

05:43 And we still need to do it for the other bond.

05:47 And we do it the same way, u equals k over q...

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