Energy of DNA Base Pairing, I. (See Exercise 21.23 . ) (a) Calculate the electric potential ener

step 1 Before we start, let me just start with the clear whiteboard. So to calculate the total potentia

Energy of DNA Base Pairing, I. (See Exercise 21.23 . ) (a)...

Key Concepts

DNA Base Pairing

DNA base pairing involves the specific hydrogen bonding interactions between complementary nucleotide bases, such as adenine pairing with thymine, and guanine pairing with cytosine. These interactions are critical for the structure and replication of DNA, as they enable the double helix to form and maintain its stability through precise arrangements of hydrogen bonds.

Hydrogen Bonding

Hydrogen bonding is a type of intermolecular force that occurs when a hydrogen atom covalently bonded to an electronegative atom, such as oxygen or nitrogen, interacts with another electronegative atom. In the context of DNA, hydrogen bonds, although weaker than covalent bonds, play a key role in holding the two strands of the double helix together by creating specific interactions between base pairs.

Electric Potential Energy

Electric potential energy is the energy a charged particle possesses due to its position in an electric field. In molecular systems, this concept is applied to calculate the energy between charged parts of molecules, such as those involved in hydrogen bonding, providing insight into the stability and energetics of molecular interactions.

Coulomb's Law

Coulomb's law quantitatively describes the electrostatic interaction between charged particles, stating that the force or potential energy between two charges is proportional to the product of their charges and inversely proportional to the distance between them. This law is fundamental in calculating the electric potential energy in various chemical bonds and molecular interactions.

Energy Scale Comparison

Comparing energy scales involves evaluating the energy of molecular interactions, such as hydrogen bonds in DNA, against fundamental atomic interactions like the electron-proton pair in the hydrogen atom. This comparison helps in understanding the relative strengths and significance of different types of bonds and interactions across scales in physics and chemistry.

Transcript

00:02 Before we start, let me just start with the clear whiteboard.

00:07 So to calculate the total potential energy for the adenine and thineine bond, we must first calculate the individual potential energies of both these molecules first.

00:18 So that the little potential energy is equal to the potential energy of the adenine bond, which is the potential energy of the nitrogen and hydrogen bonds.

00:34 Plus the potential energy of the timing bond, which is the o, hold on, let me go back and find out.

00:42 So the o, hydrogen, and nitrogen bonds.

00:47 So this is the final, this is what the final expression should look like, so we should find out the total potential energy by some, by the sum of the individual potential energies for both these molecules.

00:59 So to calculate the potential energies of these individual molecules, to start with this first.

01:04 So, or actually let's start with the thiamine bonds.

01:10 So this first, so the potential energy of the bonds between hydrogen, nitrogen and oxygen, is equal to, once again, it's equal to the individual bonds between these atoms.

01:25 So it's the potential energy of the oh bond plus the potential energy of the hydrogen and nitrogen bonds.

01:38 So now, like if you plug in the expressions for, which is, which are equivalent to the potential energies, we find out that is equal to, so the expressions that we use to calculate potential energy is coolants law, which is equal to coolants constant times charge one, times charge two over the radius between the two, or the distance between the two atoms, between the two nuclei of the atoms actually and it's called the radius between the two molecules so it's the radius in this case of the over the distance between the nuclear of the oxygen and the nuclear of the hydrogen which is which we call radius plus the cool and stop for the second second potential energy of the hydrogen and nitrogen one once again that's the chart the two charges over the distance between the two nuclei the radius so, now we have the expressions, all we need to do is just plug in values.

02:48 So if we go here and just, and we can actually factor out a couple constants since both these expressions have similar, have the same constants for in certain cases.

03:01 So we can just pull them out and make the, make a factored expression.

03:05 So it's the coolum's constant.

03:07 Let's just plug in the values as well.

03:09 So let's start with coolum's constant, which is negative 1 .6 times 10 to the columns.

03:15 Negative 19.

03:19 Once again, we see that the charges in both these expressions, there is one charge that is there in both these expressions, which is the charge of the hydrogen atom, which is equal to 9 times 10 to the power of 9.

03:39 Now that the common terms are taken out, we can finish the expression.

03:46 So the charge of the second one is negative.

03:50 Is 1 .69, 1 .6 times 10 to the power of negative 19 over the radius of the oh, which is 0 .28.

04:03 So these are actually just constants, so you should have some place to refer to refer to find these radiuses between the molecules since they're just constants and there's, there's constant.

04:17 So you should have some sort of reference when you're doing these types of problems.

04:20 So it's 0 .28 times 10 to the power of.

04:23 Let me check again, negative 9.

04:26 So then if you do plus this.

04:29 So now the second part, which is just, again, 1 .6 times 10 to the power of 19, negative 19, over the radius between the two bonds, which is 0 .5, between the two atoms, which is 0 .178 times.

05:02 10 to the negative 9.

05:08 All right.

05:10 So now if you plug the central calculator, we find out that the potential energy of the oh of the thymine or the et, this is the thymine.

05:20 Let me just remember.

05:22 Oh, this is the adamine bond, which is equal to negative 4 .45.

05:36 Let's just put this in time to pick notation, so that's easier for us, understand.

05:40 Negative 4 .45 times 10, oh, it's actually sorry, i'm getting ahead of myself there.

05:48 That's actually negative 5 .32 times 10 to the negative 19 jewels.

06:08 So now that's the first molecule.

06:10 So now moving on to the second one.

06:13 We have the adamine bond, which is once again equal to the individual potential energies...

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