Question:
The density of copper is $ 9 \times 10^3\, kg/m^3 $ and its atomic mass is $ 63.5\, u $ . Each copper atom provides one free electron. Estimate the number of free electrons per cubic metre in copper,
The density of copper is $ 9 \times 10^3\, kg/m^3 $ and its atomic mass is $ 63.5\, u $ . Each copper atom provides one free electron. Estimate the number of free electrons per cubic metre in copper,
Updated On: Jun 14, 2022
- $ 10^{19} $
- $ 10^{23} $
- $ 10^{25} $
- $ 10^{29} $
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The Correct Option is D
Solution and Explanation
Density of copper,
$\rho =9\times 10^{3} kg/m^{3}$
$=9\times 10^{6} g/m^{3}$
Avogadro number, $N_{A}=6.023\times10^{23}$
Mass of $1$ mole of copper atom, $M=63.5\,g$
Thus, number of free electrons per volume is
$n=\frac{N_{A}}{M} \rho=\frac{6.023\times10^{23}}{63.5}\times9\times10^{6}$
$=8.5 \times 10^{28}\,m^{-3}$
$\rho =9\times 10^{3} kg/m^{3}$
$=9\times 10^{6} g/m^{3}$
Avogadro number, $N_{A}=6.023\times10^{23}$
Mass of $1$ mole of copper atom, $M=63.5\,g$
Thus, number of free electrons per volume is
$n=\frac{N_{A}}{M} \rho=\frac{6.023\times10^{23}}{63.5}\times9\times10^{6}$
$=8.5 \times 10^{28}\,m^{-3}$
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Concepts Used:
Electric Current
Defining Electric Current
It is the rate of flow of electrons in a conductor. SI Unit - Ampere (A).
Electrons are negatively charged particles hence when they move a number of charges moves.
Note:- The ability of a particular substance to conduct electricity depends on the number of electrons that are able to move . Some of the materials allow current to flow better than others.
What is an Electromotive Force?
If a force acts on electrons to make them move in a particular direction, then up to some extent random motion of the electrons will be eliminated. An overall movement in one direction. The force which acts on the electrons to move them in a certain direction is known as electromotive force and its quantity is known as voltage and is measured in V.