Need help fixing this homework problem? any explanations would also be greatly a

Question

Need help fixing this homework problem? any explanations would also be greatly appreciated!

Neurons are components of the nervous system of the body that transmit signals as electrical impulses travel along their length. These impulses propagate when charge suddenly rushes into and then out o part of the neuron called an axon. Measurements have shown that, during the inflow part of this approximately 5.6x 1011 Na"(sodium ions) per meter enter the axon. a. How many coulombs of charge enter a 1.5 cm length of the non during this process? 70mV, how much b. If the potential difference between the outer and inner membrane of the axon is is required to move a single sodium ion across the membrane? W F41 and ne the electric field (magnitude c. If the membrane is approximately 7.5 nm thick, determi e physical property of the material inside the cell membrane is very similar to that of oil. d. What is the maximum potential difference that this membrane can withstand? 7. A particle possessing a charge of +2mC and a mass f I g is initially at rest when it is exposed to a uniform electrije field with strength 2 V/m. How far will the particle move in 15 s?

Explanation / Answer

a)We know that

e = 1.6 x 10^-19 C

5.6 x 10^11 per m, so in 1.5 cm

n = 0.015 x 5.6 x 10^11 = 8.4 x 10^9 Na+ ions

Now this many will have charge equal to

Q = n e

Q = 8.4 x 10^9 x 1.6 x 10^-19 = 1.344 x 10^-9 C

Hence, Q = 1.344 x 10^-9 C = 1.344 nC

b)work required will be equal to the electrostatic potential energy

PE = q V

PE = 1.6 x 10^-19 x 70 x 10^-3 = 1.12 x 10^-20 J

Hence, PE = 1.12 x 10^-20 J

c)E = V/d

E = 70 x 10^-3/7.5 x 10^-9 = 9.33 x 10^6 v/M

Hence, E = 9.33 x 10^6 V/m

d)V = kq/d

V = 9 x 10^9 x 1.6 x 10^-19/7.5 x 10^-9 = 192 milli volt

for a single ion

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