Question
Question: Assume that each atom of copper contributes one free electron. The density of copper is \(9gc{m^{ - ...
Assume that each atom of copper contributes one free electron. The density of copper is 9gcm−3 and the atomic weight of copper is 63. If the current flowing through a copper wire of 1mm diameter is 1.1ampere, the drift velocity of electrons will be:-
(A)0.01mms−1
(B)0.02mms−1
(C)0.2mms−1
(D)0.1mms−1
Solution
In order to solve this question firstly we will write the expression for finding the drift velocity of the electrons. Then we will find the required quantities and convert them into SI units. On putting all these values in the expression of drift velocity, we will arrive at the solution.
Complete answer:
In this question we are given that,
Density of copper =9cm3g
Atomic weight =63
Current flowing =1.1A
Diameter of the wire =1mm
The number of copper atoms =6.022×1023 (the number of copper atoms is equal to the number of copper electrons)
We also know that,
density=volumemass
On rearranging the above expression, we get,
volume=densitymass
On putting the required value of mass and density, we get,
volume=963
volume=7cm3
On converting the above value into SI unit, we get,
volume=7×10−6m3
Now, we can find the value of n,
n=7×10−66.022×1023
n=0.86×1029
Area is given by the expression,
A=πr2
A=3.14×(0.5×10−3)2
On solving the above value, we get,
A=0.78×10−6m3
We know that the formula of drift velocity is given by the expression,
vd=neAI
On substituting the required values in the above expression, we get,
vd=0.86×1029×1.6×10−19×0.785×10−61.1
On further solving the above value, we get,
vd=0.1smm
So, the correct answer is (D)0.1mms−1.
Note:
Various types of subatomic particles like electrons move in any random direction all the time. When these electrons are subjected to an electric field, then they do continue to move randomly, but they slowly drift in one particular direction, in the direction of the electric field applied. This net velocity at which the electrons start to drift is known as drift velocity.