Final answer:
The electric energy stored in an 8-cm-long axon at the resting potential can be calculated using the formula for capacitance. Converting the units to picojoules allows us to determine the amount of electric energy stored in the axon. The answer is approximately 3.92 pJ.
Step-by-step explanation:
The electric energy stored in an 8-cm-long axon at the resting potential can be calculated using the formula for capacitance, which is given by C = κ * A / d, where κ is the capacitance of the lipid bilayer, A is the surface area of the axon, and d is the thickness of the axon. Given that κ = 7 and d = 8 nm, we can calculate the surface area of the axon by multiplying its length by the circumference of the axon, which is given by 2 * π * r, where r is the radius of the axon. Assuming the axon is cylindrical, we can use the formula for the area of a circle to calculate the surface area, which is given by π * r^2. Once we have the surface area, we can use the formula for the capacitance to calculate the electric energy stored in the axon.
To calculate the electric energy to the nearest picojoule, we need to convert the units to the appropriate form. 1 pJ = 1 x 10^-12 J. Therefore, we can multiply the electric energy in joules by 10^12 to convert it to picojoules.
Calculation:
- Convert the thickness of the axon from nm to m: d = 8 nm = 8 x 10^-9 m
- Calculate the radius of the axon: r = 8 cm / 2 = 4 cm = 0.04 m
- Calculate the surface area of the axon: A = π * r^2 = 3.14 * (0.04 m)^2 = 0.005024 m^2
- Calculate the capacitance of the axon: C = κ * A / d = 7 * 0.005024 m^2 / 8 x 10^-9 m = 4390 F
- Calculate the electric energy stored in the axon: E = 0.5 * C * V^2, where V is the resting potential = 0.07 V
- Convert the electric energy to picojoules: E(pJ) = E(J) x 10^12 = (0.5 * 4390 F * (0.07 V)^2) x 10^12 = 3.92 pJ (to the nearest pJ)
Therefore, the electric energy stored in an 8-cm-long axon at the resting potential is approximately 3.92 pJ (option a).