If you are unfamiliar with this formalism, consult, for example, Goldstein (1977) or work throug

If you are unfamiliar with this formalism, consult, for...

Key Concepts

Analytical Mechanics

This approach redefines classical mechanics through a mathematical framework that uses generalized coordinates and energy functions like the Lagrangian and Hamiltonian. It provides a systematic way to derive the equations of motion and analyze dynamical systems, allowing for a deeper understanding of physical laws beyond the Newtonian formulation.

Quantum Mechanics Formalism

This mathematical structure of quantum theory uses concepts like Hilbert spaces, state vectors, and operators to describe physical systems. It includes the use of Dirac’s bra-ket notation and provides the rules for calculating probabilities and observables, forming the backbone of modern quantum mechanics.

Transcript

00:01 Alright, so we're tasked with estimating the nf bond length in fno2.

00:06 So we're going to have to do two things.

00:08 The first one is draw fno2.

00:11 And the second one is since this is a heteronuclear bond, we're going to have to add one half of each homonuclear bond.

00:19 So that means that since this is a, b, you're going to take one half a, a, plus one half b, right, to estimate the bond length of the bond.

00:31 This so we're gonna need the bond lengths for n to n and then f to f right which is gonna be into n is 145 picometers and then the bond lengths and then f to f is 143 picometers now this is assuming their single bond that is a single bond that we'll see we're gonna have to do from here but it should be we should be able to use a single bond to make this right here so the first thing we should try to make sure that everything, you know, and f is single bonded.

01:12 So we're going to do f and o2, so it should be f and then oo.

01:16 Total number of valence selection.

01:19 So flooring is 7 plus nitrogen is 5, plus oxygen is 6 times 2 because there's two of them.

01:29 That's going to give you 24.

01:37 And then, so we connect 2, 4, 6, we have u6.

01:41 So now we have 18 and we distribute you from the outside.

01:44 Into 4, 6, 8, 10, 12, 14, 16, 18.

01:52 We have used all the electrons.

01:54 So now we check that everything has 8 valence electrons around it...