Question

The current supplied by a battery as a function of time is ) -(0.64 A)e-/(6.0 hr). What is the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead? (e = 1.60 x 10-19 C) 3.2 x 1022 3.8 x 1023 8.6 1022 2.4 1019

Answer 1

Answer:

The total number of electrons is $8.6\times10^{22}$

(3) is correct option.

Explanation:

Given that,

The current equation is

$I=0.64 e^{\dfrac{-t}{6.0 hr}}$

We know that,

The formula of charge

$q=\int_{0}^{\infty}{I dt}$

$q=\int_{0}^{\infty}{0.64 e^{\dfrac{-t}{6.0 hr}}dt$

$q=0.64\int_{0}^{\infty}{e^{\dfrac{-t}{6.0 hr}}dt$

$q=0.64\int_{0}^{\infty}{e^{\dfrac{-t}{21600}}dt$

$q=0.64(21600e^{\dfrac{-t}{21600}})_{0}^{\infty}$

$q=0.64(0-21600)$

$q=0.64\times21600$

$q=13824\ C$

We need to calculate the number of electron

Using formula of charge

$q=ne$

$n=\dfrac{q}{e}$

$n=\dfrac{13824}{1.6\times10^{-19}}$

$n=8.6\times10^{22}$

Hence, The total number of electrons is $8.6\times10^{22}$