The moment of inertia, IB, of ^127 I^35 Cl is 2.45 ×10^-45 kg m^2 . What is the I-Cl bond distan

step 1 Okay, so this question is also about the moment of an end here. Let's first write down the equat

The moment of inertia, IB, of ^127 I^35 Cl is 2.45 ×10^-45...

The moment of inertia, $I_{B},$ of $^{127} \mathrm{I}^{35} \mathrm{Cl}$ is $2.45 \times 10^{-45} \mathrm{kg} \mathrm{m}^{2} .$ What is the I-Cl bond
distance? (Accurate masses: $^{127} \mathbf{I}=126.90$ $\left.^{35} \mathrm{Cl}=34.97 .\right)$

Key Concepts

Moment of Inertia

The moment of inertia is a physical quantity that represents an object's resistance to rotational acceleration about an axis. In molecular physics, it depends on how the mass is distributed relative to the axis of rotation. For diatomic molecules, the moment of inertia is determined by the masses of the two atoms and the square of the distance (bond length) between them.

Reduced Mass

Reduced mass is a concept that simplifies the analysis of two-body problems by replacing them with a single mass that captures the inertial properties of the system. It is calculated using the formula ? = (m1 * m2) / (m1 + m2) and is crucial in determining the moment of inertia for a diatomic molecule.

Rigid Rotor Model

The rigid rotor model is a simplified model in molecular spectroscopy that assumes a diatomic molecule rotates without any change in the bond length. This assumption allows the use of simple formulas to relate the moment of inertia to the bond distance, making it easier to calculate the bond length from rotational data.

Bond Length Calculation

Bond length calculation in the context of molecular rotational dynamics involves using the relationship I = ?r^2, where I is the moment of inertia and ? is the reduced mass. By rearranging this equation, the bond distance (r) can be obtained once the moment of inertia and the reduced mass are known.

Mass Conversion

Accurate mass conversion is essential in physical calculations, as atomic masses are often given in atomic mass units (amu) but the equations in rotation dynamics require masses in kilograms. Converting these values appropriately ensures that the calculations of reduced mass and moment of inertia yield correct and consistent results.

Transcript

00:02 Okay, so this question is also about the moment of an end here.

00:09 Let's first write down the equation, the formula, to how to calculate the moment of in it here.

00:18 So i equals to the reduced mass of molecule times the bound distance square in that molecule.

00:29 And this question, it asks, what is the bond distance? it asks the distance, this one, right? so we can just rearrange this equation.

00:42 Let's just rearrange it.

00:44 R squared equals to the moment of inert here over the reduced mass.

00:55 So the bond distance is equal to square root.

00:59 I over the reduced mass.

01:08 So if we look at the question, the i, the moment of inner tier is given, right? which is 2 .45 times 10 to minus 45.

01:28 And if we can know the reduced mass of this molecule, and we can calculate the bond distance.

01:40 So now, all we need to do is to just calculate the reduced mass.

01:45 And let's recall the reduced mass equals to, in the two atom molecule, right? m1 times m2 over m1 plus m2.

02:01 M1 is iodine, and m2 is chlorine.

02:06 So that's right on the m1 is 126 .9 times 1 .66 times 10 to minus 27 times the mass of the chlorine, which is 34 .97, 1 .66x6 times 10 to minus 27.

02:40 Over, same, right, but it's addition 1 .6 times 1 .66 times 10 to minus 7 plus...

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