Question $1(1$ point$)$

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Example: A container holds a gas at a temperature T$.$ The molecules in the gas have two energy states E$1=0\mathrm{.}50$kBT and E$2=0\mathrm{.}80$kBT$.$ If the container holds $100$ molecules, how many of them will be in state E$2?$

Question $1$ options:

$57$

$43$

$26$

$74$

Question $2(1$ point$)$

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A block of mass $86\mathrm{.}5$ kg is partially submerged in water. If the block has dimensions of W $=0\mathrm{.}550$ m$,$ L $=0\mathrm{.}700$ m$,$ and H$=1\mathrm{.}50$ m what percent of the box will be underwater when submerged? The depth D is the amount submerged. Give your answer in percent to $1$ decimal place. Do NOT include the percent symbol.$$

Your Answer:

Question $2$ options:

Your Answer

Question $3(1$ point$)$

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In an experiment similar to Perrin's it is observed that there are $118$ particles per unit volume at a height of $5\mathrm{.}20$ mm $,$ and $50$ particles per unit volume at a height of $12\mathrm{.}7$ mm$.$ How many particles per unit volume would you expect to see near the bottom of the column? Round your answer to the nearest whole particle.

Your Answer:

Question $3$ options:

Your Answer

Question $4(1$ point$)$

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Spherical particles which are suspended in a liquid have a certain terminal velocity under the force of gravity. They are then placed in a centrifuge of radius $5\mathrm{.}00$ cm$.$ At what frequency must the centrifuge rotate in order for the terminal velocity of the particles to be equal to their terminal velocity under the force of gravity?

Question $4$ options:

$3\mathrm{.}94$ Hz

$1\mathrm{.}96$ Hz

$2\mathrm{.}23$ Hz

$4\mathrm{.}96$ Hz

Question $5(1$ point$)$

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Spherical proteins of an unknown radius have a density of $5\mathrm{.}40$ x $103$kg$/$m$3$ and are suspended in blood which has a viscosity $3\mathrm{.}5$ times that of water. The mixture is placed in a centrifuge of radius $14\mathrm{.}6$ cm which spins at $9000$ rpm$.$ If the proteins have a terminal velocity of $4\mathrm{.}10$ x$10-6$m$/$s$,$ what is their radius? Express your answer to two decimal places in units of nanometers $(1$x$10-9$m$),$ but do not include units in your answer.