Question

If a current of 1.5 ampere flows through a metallic wire for 3 hours. Then how many electrons would flow through the wire?
(A) \[2.25\times {{10}^{22}}\] electrons
(B) \[1.13\times {{10}^{23}}\] electrons
(C) \[1.01\times {{10}^{23}}\] electrons
(D) \[4.5\times {{10}^{23}}\] electrons

Answer 1

Hint:The equation to calculate charge is Charge Q = Current (I) \[\times \]Time (T).
One faraday is equal to 96500 C.
1 Faraday = 96500 Columbus (C) = 1 mole of electron = Avogadro number (\[{{N}_{A}}=6.023\times {{10}^{23}}\])

Complete step by step solution:
In the question it is given that 1.5 ampere current flows through the metallic wire for three hours.
We know that one faraday is equal to 96500C.
1 F = 96500C = 1 mole of electron
               = Avogadro number (\[{{N}_{A}}=6.023\times {{10}^{23}}\])
We know that Charge Q = Current (I) \[\times \]Time (T)
Current (I) = 1.5 ampere
Time (T) = 3 hours (180 minutes = 10,800 sec)
Therefore, \[\begin{align}
  & Q=I\times T \\
 & \text{Q = 1}\text{.5 }\times \text{ 10,800 } \\
 & \text{Q = 16,200} \\
\end{align}\]
We know that ,
\[\begin{align}
  & 96500\text{ C }\xrightarrow{{}}6.023\times {{10}^{23}} \\
 & \\
 & 1\text{ C }\xrightarrow[{}]{}\frac{6.023\times {{10}^{23}}}{96500} \\
 & \\
 & 16,200\text{ C }\xrightarrow{{}}\frac{6.023\times {{10}^{23}}}{96500}\times 16,200 \\
 & \\
 & =1.01\times {{10}^{23}}\text{ electrons} \\
\end{align}\]

So, the correct option is C.

Note: Don’t be confused between the electric charge and current. Both are not the same.
Electric charge: “Electric charge is the physical property of a substance that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges, positive charge (carried by protons) and negative charge (carried by electrons). Like charges means the same charge repels each other and unlike charges (opposite charges) attract each other”.
Current: “An electric current is said to exist when there is a net flow of electric charge through a region. Electric charge is carried by charged particles, so an electric current is a flow of charged particles”.