Answer:
The total number of electrons is [tex]8.6\times10^{22}[/tex]
(3) is correct option.
Explanation:
Given that,
The current equation is
[tex]I=0.64 e^{\dfrac{-t}{6.0 hr}}[/tex]
We know that,
The formula of charge
[tex]q=\int_{0}^{\infty}{I dt}[/tex]
[tex]q=\int_{0}^{\infty}{0.64 e^{\dfrac{-t}{6.0 hr}}dt[/tex]
[tex]q=0.64\int_{0}^{\infty}{e^{\dfrac{-t}{6.0 hr}}dt[/tex]
[tex]q=0.64\int_{0}^{\infty}{e^{\dfrac{-t}{21600}}dt[/tex]
[tex]q=0.64(21600e^{\dfrac{-t}{21600}})_{0}^{\infty}[/tex]
[tex]q=0.64(0-21600)[/tex]
[tex]q=0.64\times21600[/tex]
[tex]q=13824\ C[/tex]
We need to calculate the number of electron
Using formula of charge
[tex]q=ne[/tex]
[tex]n=\dfrac{q}{e}[/tex]
[tex]n=\dfrac{13824}{1.6\times10^{-19}}[/tex]
[tex]n=8.6\times10^{22}[/tex]
Hence, The total number of electrons is [tex]8.6\times10^{22}[/tex]
