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 He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas).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 ± 0.005)m, the gas in the tube is (Useful information: = 640 J1/2 mole–1/2; = 590 J1/2 mole–1/2. The molar masses M in grams are given in the options. Take the values of for each gas as given there.)

Engineering

Physics

Quinkes Kundts and Resonance Tube Experiment

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 He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas).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

$Oxygen (M = 32, \sqrt{\frac{10}{32}} = \frac{9}{16})$

$Nitrogen (M = 28, \sqrt{\frac{10}{28}} = \frac{3}{5})$

$Argon (M = 36, \sqrt{\frac{10}{36}} = \frac{17}{32})$

$Neon (M = 20, \sqrt{\frac{10}{20}} = \frac{7}{10})$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

λ = 1.4

v = fλ = 244 × 1.4 = 341.6

$error = \frac{5}{350} \underline{~} 1.3 %$

v = 341.6 ± 4.88

336.72 < v < 346.48

$v_{mono} = \sqrt{\frac{γRT}{M}} = \sqrt{\frac{1 .6 7 RT}{20 \times 10^{- 3}}}$

$v_{Ne} = \sqrt{167 RT} \times \sqrt{\frac{10}{20}} = 640 \times \frac{7}{10} = 448$