A resonance column uses a tuning fork of frequency 244 s⁻¹. The tube contains an unknown gas. The minimum resonant height is (0.350 ± 0.005) m. Useful data: √(167RT) = 640 J¹ᐟ² mol⁻¹ᐟ² and √(140RT) = 590 J¹ᐟ² mol⁻¹ᐟ². Identify the gas.
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Question

A resonance column uses a tuning fork of frequency 244 s⁻¹. The tube contains an unknown gas. The minimum resonant height is (0.350 ± 0.005) m. Useful data: √(167RT) = 640 J¹ᐟ² mol⁻¹ᐟ² and √(140RT) = 590 J¹ᐟ² mol⁻¹ᐟ². Identify the gas.

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G1 Physics · Accepted Answer

Step 1: Open-open pipe: fₙ = nv/(2effective length). Closed-open pipe: fₙ = (2n−1)v/(4effective length). Step 2: Include end correction in effective length where stated; successive resonances differ by λ/2. Step 3: Apply the harmonic/resonance condition. Final: D: Argon: M = 36, √(10/36) = 17/32.