The rotational lines seperation in Raman experiment for HC1molecule is 41.6 cm-1The inter nuclear distance is________ÅCorrect answer is between '1.25,1.32'. Can you explain this answer?

Question

The rotational lines seperation in Raman experiment for HC1molecule is 41.6 cm-1The inter nuclear distance is________&Aring;Correct answer is between '1.25,1.32'. Can you explain this answer?

Answer

We can use the formula for the rotational lines separation:

Δν = 2B

where Δν is the separation between two adjacent rotational lines and B is the rotational constant, given by:

B = h/(8π2cI)

where h is Planck's constant, c is the speed of light, and I is the moment of inertia of the molecule. For HCl, the moment of inertia is:

I = μr^2

where μ is the reduced mass of the molecule and r is the internuclear distance. The reduced mass is given by:

μ = m1m2/(m1 + m2)

where m1 and m2 are the masses of the hydrogen and chlorine atoms, respectively. Substituting these values, we get:

B = h/(8π2cμr^2)

Δν = h/(4π2cμr^2)

Solving for r, we get:

r = √(h/(4π2cμΔν))

Substituting the given values, we get:

r = √(6.626x10^-34 J s/(4π^2x3x10^8 m/sx(1.0079+35.453) kg/mole x41.6 s^-1))

r = 1.275x10^-10 m

Therefore, the internuclear distance of HCl is 1.275x10^-10 m.

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