Question

Calculate the moment of inertia for HCl molecule from the given value of rotational
constant, B = 10.40 cm
(A) 2.68x10-47 kg m
(B) 4.21x10-5 kg m
(C) 2.68 x 10-31 kg m
(D) 4.21x10+? kg m
​

Answer 1

Correct options:

(A)  2.69×10⁻⁴³ kg m²

(B) 4.21×10⁻⁵ kg m²

(C) 2.68×10⁻³¹ kg m²

(D) 4.21×10 kg m²

Answer:

The moment of inertia of HCl molecule with a rotational constant 10.40cm is (A) 2.69×10⁻⁴³ kg m².

Explanation:

Given:

Rotational constant (B) = 10.40cm = 0.1040m

To find:

Moment of inertia (I) =?

Formula:

$B = \frac{h}{8\pi ^2cI}$

Solution:

Using the rotational constants from the polynomial curve fit with the definition of B gives the moment of inertia as follows:

$I = \frac{h}{8\pi^2cB}$

where, I is the moment of inertia, h is the Planck's constant, c is the speed of light, and B is the rotational constant.

Substituting the respective values, we get

$I = \frac{6.63*10^{-34}}{8*(3.14)^2*3*10^8*0.1040}$

$I = \frac{6.63*10^{-34}}{2.461*10^9}$

I = 2.69×10⁻⁴³ kg m²

Therefore, the moment of inertia for HCl molecule is 2.69×10⁻⁴³ kg m².

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Answer 2

The moment of inertia for HCl molecule is 2.68x10-47 kg m.

Given:

Rotational constant (B) = 10.40cm = 0.1040m

To find:

Moment of inertia (I) =?

Solution:

Using the rotational constants from the polynomial curve fit with the definition of B gives the moment of inertia as follows:

I = (6.626 x 10^-34 J s) / (8π^2 x 10.40 cm^-1)= 2.68 x 10^-47 kg m^2

where, I is the moment of inertia, h is the Planck's constant, c is the speed of light, and B is the rotational constant.

Substituting the respective values, we get

I = 2.69×10⁻⁴³ kg m²

Therefore, the moment of inertia for HCl molecule is 2.69×10⁻⁴³ kg m².

The moment of inertia is a measure of the molecule's resistance to rotational motion. It depends on the distribution of mass in the molecule and the distance of the mass from the axis of rotation. In general, more massive and compact molecules will have higher moment of inertia values than lighter and more spread-out molecules.

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