Final answer:
The energy stored in the cell is approximately 2.556 * 10^-16 joules.
Step-by-step explanation:
The energy stored in a cell can be calculated by using the formula: E = 0.5 * C * V^2, where E is the energy stored, C is the capacitance, and V is the voltage.
Since the cell membrane is being modeled as a capacitor, we can use the equation for the capacitance of a spherical capacitor: C = (4 * pi * epsilon * r) / d, where C is the capacitance, pi is a mathematical constant, epsilon is the permittivity of the medium between the capacitor plates, r is the radius of the capacitor plates, and d is the distance between the plates.
Plugging in the given values, we have: C = (4 * pi * epsilon * r) / d = (4 * 3.14 * 8.854 * 10^-12 * 8 * 10^-6) / 7 * 10^-9.
Now, we can substitute the value of C and the voltage (-90 mV) into the energy equation to calculate the energy stored in the cell: E = 0.5 * C * V^2 = 0.5 * (4 * 3.14 * 8.854 * 10^-12 * 8 * 10^-6) / 7 * 10^-9 * (-90 * 10^-3)^2 = 2.556 * 10^-16 J.
Therefore, the energy stored in the cell is approximately 2.556 * 10^-16 joules.