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Chapter 4: Q49E (page 844)

Pure silicon at room temperature contains approximately1.0脳1016 free electrons per cubic meter. (a) Referring to Table 25.1, calculate the mean free time for蟿 silicon at room temperature. (b) Your answer in part (a) is much greater than the mean free time for copper given in Example 25.11. Why, then, does pure silicon have such a high resistivity compared to copper?

Short Answer

Expert verified
  1. The mean time for蟿 silicon at room temperature is 1.55脳10-12s.
  2. Silicon has greater than the mean free for cooper.

Step by step solution

01

Define the ohm’s law, resistance (R) and power (P).

The average time between the collisions for the electron is known as mean free time 蟿.

蟿=mne2蚁

Where, is charge of the electron which is equal to 1.6脳10-19C, is the mass of electron which is equal to 9.11脳10-31kg,n is concentration and蚁 is resistivity.

02

Determine the mean free time.

The resistivity 蚁of silicon is equal to 2300惟路mand the

The mean free time for silicon is

蟿=mne2蚁=9.11脳10-311.0脳10161.6脳10-192300=1.55脳10-12s

From the expression蟿=mne2蚁 the mean free time is inversely proportional to concentration n.

蟿鈭�1n

As the silicon has less valuen than the copper. So, silicon has larger value.

Hence, mean free time蟿 for silicon at room temperature is1.55脳10-12s and silicon has greater than the mean free for cooper.

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