Question

A student is performing an experiment using a resonance column and a tuning fork of frequency $244 \,s ^{-1}$. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $(0.350\, \pm 0.005) \,m$, the gas in the tube is
(Useful information: $\sqrt{167 RT }=640\, J ^{1 / 2} \,mole ^{-1 / 2} ; \sqrt{140 \,RT }=590\, J ^{1 / 2}\, mole ^{-1 / 2}$.
The molar masses $M$ in grams are given in the options. Take the values of $\sqrt{\frac{10}{ M }}$ for each gas as given there.)

• A. Neon $\left( M =20, \sqrt{\frac{10}{20}}=\frac{7}{10}\right)$
• B. Nitrogen $\left(M=28, \sqrt{\frac{10}{28}}=\frac{3}{5}\right)$
• C. Oxygen $\left(M=32, \sqrt{\frac{10}{32}}=\frac{9}{16}\right)$
• D. Argon $\left( M =36, \sqrt{\frac{10}{36}}=\frac{17}{32}\right)$

Answer 1

Answer: (D)

$\ell=\frac{1}{4 v} \sqrt{\frac{\gamma RT }{ M }}$
Calculations for $\frac{1}{4 v} \sqrt{\frac{\gamma RT }{ M }}$ for gases mentioned in options $A, B, C$ and $D$, work out to be $0.459 \,m , 0.363\, m\,0.340\,m \& 0.348\, m$ respectively. As $\ell=(0.350 \pm 0.005) \,m ;$