Discussion Forum

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 He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas).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)

$\sqrt{167RT}=640J^{1/2}mol^{-1/2}$

$\sqrt{140RT}=590J^{1/2}mol^{-1/2}$. The molar masses M in grams are given in the options. Take the value of 

$\sqrt{10/M}$  for each gas as given there.)

Answer:

Explanation:

Minimum  length  =  $\frac{\lambda}{4}\Rightarrow\lambda=4l$

 Now, v=f ,   $\lambda=(244)\times 4\times l$

  as        $l=0.350\pm0.005$

$\Rightarrow$    v lies between 336.7 m/s to 346.5 m/s

  Now,   $v=\sqrt{\frac{\gamma RT}{M\times 10^{-3}}}$  , here M is

 Molecular  mass in gram

                  $=\sqrt{100\gamma RT}\times\sqrt{\frac{10}{M}}$

 For  monoatomic gas 

       $\gamma=1.67$

 $\Rightarrow$      $v=640\times \sqrt{\frac{10}{M}}$

For diatomic gas,

      $\gamma=1.4\Rightarrow v=590\times\sqrt{\frac{10}{M}}$

  $\therefore$     $V_{Ne}=640\times \frac{7}{10}=448 m/s$

                        $V_{Ar}=640\times \frac{17}{32}=340 m/s$

                           $V_{O_{2}}=590\times \frac{9}{16}=331.8 m/s$

                                  $V_{N_{2}}=590\times \frac{3}{5}=354 m/s$

$\therefore$   only possible answer is Argon