A slice of germanium of cross-sectional area 1.0 cm2 carries a current of 56 μA. The number density of charge carriers in the germanium is 2.0 × 1013 cm-3

Question 15

A slice of germanium of cross-sectional area 1.0 cm² carries a current of 56 μA. The number density of charge carriers in the germanium is 2.0 × 10¹³ cm^-3. Each charge carrier has a charge equal to the charge on an electron.

What is the average drift velocity of the charge carriers in the germanium?

A 0.18 m s^-1                     B 18 m s^-1                         C 180 m s^-1                       D 1800 m s^-1

Reference: Past Exam Paper – June 2018 Paper 13 Q30

Solution:

Answer: A.

I = nqAv

Drift velocity v = I / nqA

We need to convert the quantities given into SI units.

Cross-sectional area A = 1.0 cm² = 1.0×10^-4 m² 

Number density n = 2.0×10¹³ cm^-3

That is, in 1 cm³, there are 2.0×10¹³ charge carriers

1 cm³ = 1×10^-6 m³

1 cm³ - - > 2.0×10¹³ charge carriers

1×10^-6 m³ - - > 2.0×10¹³ charge carriers

1 m³ - - > (2.0×10¹³) / (1×10^-6) = 2.0×10¹⁹ charge carriers

So, number density n = 2.0×10¹³ cm^-3 = 2.0×10¹⁹ m^-3

Drift velocity v = I / nqA

Drift velocity v = (56×10^-6) / (2.0×10¹⁹ × 1.6×10^-19 × 1.0×10^-4)

Drift velocity v = 0.175 m s^-1 = 0.18 m s^-1