Question

The moment of inertia of HCL molecules about an axis passing through its centre of mass and perpendicular to the line joining the H+ and CL- ions will be, if the interatomic distance is 1A°



(sub- physics, topic- system of particles and rotatary motion)​

Answer 1

$\large\bold{\underline{\underline{Question:-}}}$

The moment of inertia of HCL molecules about an axis passing through its centre of mass and perpendicular to the line joining the H+ and CL- ions will be, if the interatomic distance is 1A°

$\large\bold{\underline{\underline{Answer:-}}}$

Mass of Cl atom$= 35.55 \times {10}^{ - 27} \: \: kg$

Mass of H atom$= 1.66 \times {10}^{ - 27} \: \: kg$

Total mass of the Molecule$=37.21 \times {10}^{ - 27} \: \: kg$

Distance between the two atoms$= {10}^{ - 10} \: \: m$

Distance from the axis of rotation,d$= 10 ^{ - 10}$

$d = 0.5 \times 10^{ - 10} \: \: m$

Moment of inertia,I = mr²

$I =37.21 \times 10 ^{ - 27} \times (0.5 \times 10 ^{ - 10} ) {2} \: \: kg. {m}^{2}$

$\boxed{ = >9.3025 \times {10}^{ - 47} \: \: kg. {m}^{2}}$

Answer 2

Given:

• HCl molecule

• Inter atomic distance between H+ and Cl- ion = 1A°

To Find :

The moment of Inertia of HCl molecules about an axis passing through HCl molecule's center of mass and perpendicular to the line joining the H+ and Cl- ions

Solution:

Formula to be used:

Inertia (I) = Mass of the system (M) x (Distance from the axis of rotation(R))²

                                             I = MR²

Now, we know that:

• Mass of the H atom = 1.66 x 10⁻²⁷ kg

• Mass of Cl atom = 35.55 x 10⁻²⁷ kg

Thus the total mass of the molecule = Mass of H atom + Mass of Cl atom

The total mass of the molecule (M) = 1.66 x 10⁻²⁷ + 35.55 x 10⁻²⁷

• M = 10⁻²⁷ ( 1.66 + 35.55)

• M =  37.21 x 10⁻²⁷ kg

Now, we know interatomic distance = 1A° = 1 x 10⁻¹⁰m

Then, the distance from the axis of rotation (R) = (1 x 10⁻¹⁰)/ 2 = 0.5 x 10⁻¹⁰m

Putting the values obtained in the given formula we get:

                        I = (37.21 x 10⁻²⁷ kg)(0.5 x 10⁻¹⁰m)²

                       I = 9.3025 x 10⁻⁴⁷ kg.m²

Thus, the moment of inertia of HCL molecules about an axis passing through its center of mass and perpendicular to the line joining the H+ and CL- ions will be  9.3025 x 10⁻⁴⁷ kg.m²