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

The total number of electrons is
`8.6*10^(22)`

(3) is correct option.

Step-by-step explanation:

Given that,

The current equation is

`I=0.64 e^{(-t)/(6.0 hr)}`

We know that,

The formula of charge

`q=\int_(0)^(\infty){I dt}`

`q=\int_(0)^(\infty){0.64 e^{(-t)/(6.0 hr)}dt`

`q=0.64\int_(0)^(\infty){e^{(-t)/(6.0 hr)}dt`

`q=0.64\int_(0)^(\infty){e^{(-t)/(21600)}dt`

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

`q=0.64(0-21600)`

`q=0.64*21600`

`q=13824\ C`

We need to calculate the number of electron

Using formula of charge

`q=ne`

`n=(q)/(e)`

`n=(13824)/(1.6*10^(-19))`

`n=8.6*10^(22)`

Hence, The total number of electrons is
`8.6*10^(22)`