the molar atomic mass of lodine is 127 g. A standing wave in a tube filled with iodine gas ta 400 K has nodes that are 6.77 cm apart when the frequency is 1000 Hz. Determine from these data whether iodine gas is monatomic or diatomic.

To know iodine gas is monoatomic or diatomic, we have to find out the value of adiabatic gas constant γ.
First we have to find out the speed v of the sound in the iodine gas.
The wavelength λ will be,
λ = 2×6.77 cm
= (2×6.77 cm) (10^-2 m/1 cm)
=2×0.0677 m
= 0.1354 m
To obtain the speed v of the sound in the iodine gas, substitute 1000 Hz for f and 0.1354 m for λ in the equation v = fλ,
v = fλ
= (1000 Hz) (0.1354 m)
= (1000 Hz) (1/1 s/1 Hz)(0.1354 m)
= 135 m/s
To obtain the value of adiabatic gas constant γ, substitute 127 g/mol for m, 135 m/s for v, 8.31 J/mol.K for R and 400 K for T in the equation γ = nmv²/RT,
γ = nmv²/RT
= n (127 g/mol) (135 m/s²)²/(8.31 J/mol.K) (400 K)
= n (127 g/mol) (10^-3 kg/1 g) (135 m/s²)²/(8.31 J/mol.K) (400 K)
= n (0.696)
As γ is greater than 1, thus n≥2.
If n= 2, then,
γ = n (0.696)
= 2 (0.696)
= 1.39 (which is consistent)
If n= 3, then,
γ = n (0.696)
= 3 (0.696)
= 2.08 (which is not consistent)
From the above observation we conclude that, iodine gas is diatomic.