Exam Krackers physics problem

[riceguard]

Can someone explain this problem to me, the answer they provided in the back doesn't match up to any of the answer options.

A cell at rest has a potential of -70mV across it's membrane. Assume the diameter of the cell is 20um. The cell membrane has a capacitance of 1uF/cm^2. Elementary charge = 1.6*10^-19C

How many potassium ions in the cell are needed to charge the cell membrane?
A. 220 ions
B. 560 ions
C. 5.6 *10^4 ions
D. 2.2*10^15 ions

The answer is C, but in the back the final value they come up with is 1.4*10^4, which is no where close to 5.6 *10^4 ions

Also does anyone know of a quicker way to get the answer instead having to plug and chug 5 different equations?

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[mcatjelly]

Have you checked their errata to see if that's a mistake on their end?

 

[riceguard]

The one mistake they made was saying 1.4*10^-4 instead of 1.4*10^4, otherwise all their numbers match up

 

[Cawolf]

The answer is C, but in the back the final value they come up with is 1.4*10^4, which is no where close to 5.6 *10^4 ions

I didn't check the math, but if that is the calculated value, C is the best choice. It is the only choice of the same magnitude.

The MCAT will require you to get comfortable with rounding.

 

[mcatjelly]

@riceguard, if you check out their online forums, they post a bunch of corrections to errors in the book. Here's their correction to that question:

For question 87, the answer explanation should be:

“Choice B is correct. Assuming the cell is a sphere, the surface area of the cell is 4 pr2 = 12.56 x (10 x 10-6)2 = 1.256 x 10-9 cm2. The capacitance of the cell membrane is: 1 µF/cm2 x 1.256 x 10-9 cm2 = 1.256 x 10-15 F. The charge that the capacitor can hold at a given voltage is Q = CV = 1.2566 x 10-15 x 70 x 10-3 = 8.8 x 10-17 C. Every potassium ion has a charge of +e, so the number of potassium ions is equal to (8.8 x 10-17) / (1.6 x 10-19) = 550 ions. Choice B is by far the closest answer and is correct. Heavy rounding can be done in this problem to accelerate calculation because the answer choices are quite different from each other.”

 

[BlueCircle]

@riceguard, if you check out their online forums, they post a bunch of corrections to errors in the book. Here's their correction to that question:

For question 87, the answer explanation should be:

“Choice B is correct. Assuming the cell is a sphere, the surface area of the cell is 4 pr2 = 12.56 x (10 x 10-6)2 = 1.256 x 10-9 cm2. The capacitance of the cell membrane is: 1 µF/cm2 x 1.256 x 10-9 cm2 = 1.256 x 10-15 F. The charge that the capacitor can hold at a given voltage is Q = CV = 1.2566 x 10-15 x 70 x 10-3 = 8.8 x 10-17 C. Every potassium ion has a charge of +e, so the number of potassium ions is equal to (8.8 x 10-17) / (1.6 x 10-19) = 550 ions. Choice B is by far the closest answer and is correct. Heavy rounding can be done in this problem to accelerate calculation because the answer choices are quite different from each other.”

This explanation is incorrect (as is the one in the book). The explanation above does not convert m^2 to cm^2. Doing the conversion turns 1.256e-9 into 1.256e-5. From there your final answer becomes 5.5e6 ions.

The answer in Examkrackers is wrong because they used the wrong conversion: they did 1m^2=100cm^2 when it should be 1m^2=10 000cm^2.


So yeah, EK dropped the ball on this one. The closest answer is two orders of magnitude smaller. I know this is a very late reply, but someone in the future will look this up and find the right answer

 

[frog301]

This explanation is incorrect (as is the one in the book). The explanation above does not convert m^2 to cm^2. Doing the conversion turns 1.256e-9 into 1.256e-5. From there your final answer becomes 5.5e6 ions.

The answer in Examkrackers is wrong because they used the wrong conversion: they did 1m^2=100cm^2 when it should be 1m^2=10 000cm^2.


So yeah, EK dropped the ball on this one. The closest answer is two orders of magnitude smaller. I know this is a very late reply, but someone in the future will look this up and find the right answer

yeah they will