Question

The atomic mass of iodine is 127 g/mol. A standing wave in iodine vapour at 400 K has nodes that are 6.77 cm apart when the frequency is 1000 Hz. At this temperature, is iodine vapour monoatomic or diatomic. Answer 1/2 for mono/diatomic

Answer 1

Given : $T=400K$, $\nu =1000Hz$
Atomic mass of Iodine $m_I=0.127kg/mol$
Let Iodine exists as $I_n$.
So molar mass of $I_n$, $M_{I_n}=nm=0.127nkg/mol$
Distance between the nodes $l=6.77cm$
So, wavelength of sound wave $\lambda =2l=2\left(6.77\right)=0.135m$
Thus, velocity of sound wave $v=\nu \lambda$
$\therefore$ $v=1000\times 0.135=135m/s$
Also, velocity of sound wave $v=\sqrt{\frac{\gamma RT}{M_{I_n}}}$
$\therefore$ $135=\sqrt{\frac{\gamma \left(8.3\right)\left(400\right)}{0.127n}}$
$⟹\gamma =0.7n$
For $n=1$, we get $\gamma =1.4$ which is for diatomic gas.
Hence, Iodine is diatomic.
Thus answer is 2.