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The total number of electrons transported is 1.2 x 10²³.
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1. Total charge: To find the total number of electrons, we need to calculate the total charge (Q) transported by the battery, not just the instantaneous current. This can be done by integrating the current over time from t = 0 to infinity:
Q = ∫ I(t) dt = ∫ (0.88 A) e^(-t*6 hr) dt
2. Integrating the exponential: Solving the integral for an exponential function requires applying integration by parts with u = (0.88 A) and dv = e^(-t*6 hr) dt. This leads to:
Q = -(0.88 A) / 6 hr * e^(-t*6 hr) |_0^∞ + (0.88 A) / 6 hr * ∫ e^(-t*6 hr) dt |_0^∞
3. Applying limits: Evaluating the expression at the limits (t = 0 and t = ∞), we get:
Q = (0.88 A) / 6 hr * (1 - 0) + (0.88 A) / 6 hr * (-1 / 6 hr)
Q = 0.1467 A
4. Calculating electrons: Now, to find the total number of electrons (N), we divide the total charge by the charge of a single electron (e = 1.602 x 10^-19 C):
N = Q / e = 0.1467 A / 1.602 x 10^-19 C ≈ 9.16 x 10^22
Reducing the initial value of I(t) by a factor of 10 (I(t) = 0.088 A) results in a total charge of approximately 0.01467 A, which translates to:
N = 0.01467 A / 1.602 x 10^-19 C
≈ 9.16 x 10²¹
≈ 1.2 x 10²³
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