Question

The internuclear distance of NaCl is 2.36 x10-10m. Calculate the reduced mass and moment of inertia of NaCl. Given atomic mases of Cl= 35 x10-3 kg mol-1 and Na =23x 10-3 kg mol-1​

Answer 1

the energetics of molecular vibration we take the simplest example, a diatomic heteronuclear molecule  AB . Let the respective masses of atoms  A  and  B  be  mA  and  mB . For diatomic molecules, we define the reduced mass  μAB  by:

Reduced mass is the representation of a two-body system as a single-body one. When the motion (displacement, vibrational, rotational) of two bodies are only under mutual interactions, the inertial mass of the moving body with respect to the body at rest can be simplified to a reduced mass.

Answer 2

Given: The internuclear distance of NaCl is 2.36 x10-10m.

To find: We have to find the reduced mass and moment of inertia of NaCl.

Solution:

Reduced mass of NaCl is given as-

$u = \frac{m \times n}{m + n}$

where m is the atomic mass of Na and n is the atomic mass of Cl.

Given atomic mases of Cl= 35 x10-3 kg mol-1 and Na =23x 10-3 kg mol-1

Thus reduced mass will be-

$u = \frac{35 \times {10}^{ - 3} \times 23 \times {10}^{ - 3} }{58 \times {10}^{ - 3} } \\ = 0.013$

Moment of inertia can be given as-

$= u {r}^{2}$

The internuclear distance of NaCl is 2.36 x10-10m.

$= 0.013 \times 2.36 \times {10}^{ - 10 } \\ = 3.06 \times {10}^{ - 12}$

The reduced mass of NaCl is 0.013kg/mol and moment of inertia is $3.06×10^{-12}kg.m^2/mol$.