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GATE 2022 CY – Question 62

Physical Chemistry · Surfaces and Interfaces: Physisorption and chemisorption. Langmuir, Freundlich and Brunauer-Emmett-Teller (BET) isotherms. Surface catalysis: Langmuir-Hinshelwood mechanism. Surface tension, viscosity, Self- assembly/ physical chemistry of colloids, micelles and macromolecules. · 2 marks · Numerical answer

The radius of gyration of a three-dimensional random-coil linear polyethylene molecule of molecular weight 840000 is ______ nm (one decimal place). C–C bond length is 0.154 nm.

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Correct answer: 15.2 to 15.6

Explanation

There are 840000/14=60000 carbon backbone units, approximately as many C–C links. For an ideal freely jointed chain, Rg²=Nb²/6.

Hence Rg=0.154√(60000/6)=**15.4nm**. This is the random-coil model intended by the key; real bond-angle/characteristic-ratio corrections would need additional data.