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Question

A current of 1.34 A exists in a copper wire of cross-section 1 mm2. Assuming that each copper atom contributes one free electron, the drift speed of the free electrons in the wire will be:
(Density of copper is 8990 kg/m3, atomic mass is 63.50 and charge on electron is 1.6×1019 C)

A
0.3 mm/s
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B
0.5 mm/s
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C
0.1 mm/s
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D
0.05 mm/s
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Solution

The correct option is C 0.1 mm/s
The density of copper is 8990 kg/m3.

Mass of 1 m3 volume of the copper is 8990 kg
i.e.m=8990×103 gm

Number of moles of copper in 1 m3 is

n=8990×103 g63.5 g/mole=1.4×105 moles

since each mole will contain NA atoms,
where NA=6.023×1023

The number of atoms in 1 m3 copper will be,

n=1.4×105×6.023×1023

n8.4×1028

Using current drift velocity relation,
I=neAvd

vd=IneA

vd=1.348.4×1028×1.6×1019×(1×(103)2)

vd=1.348.4×1.6×103=0.997×104

vd104 m/s=0.1 mm/s

Hence, option (c) is correct.

Why this question ?Tip :In the question it has been given that1 electron is contributed per atom, this gives the hint to find the number of atoms in given volume of copper using mole-concept.

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