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In a semiconductor material (1//5)th of ...

In a semiconductor material `(1//5)`th of the total current is carried by the holes and the remaining is carried by the electrons. The drift speed of electrons is twice that of holes at this temperature. Thr ratio between the number densities of electrons and holes is

A

`(21)/(6)`

B

5

C

`(3)/(8)`

D

2

Text Solution

Verified by Experts

The correct Answer is:
D
If I is the total current, then
Current carried by the holes, `I_(h)=(I)/(5)I` and that carried by the electrons, `I_(e)=(4)/(5)I`
If `n_(e)andn_(h)` are the number densities of electrons and holes respectively, then
`I_(e)=n_(e)Aev_(e)andI_(h)=n_(h)Aev_(h)`
`therefore (I_(e))/(I_(h))=(n_(e)Aev_(e))/(n_(h)Aev_(h))or(n_(e))/(n_(h))=(I_(e))/(I_(h))(v_(h))/(v_(e))`
`becauseI_(e)=(4)/(5)I,I_(h)=(1)/(5)I,v_(e)=2v_(h).therefore(n_(e))/(n_(h))=((4/5I))/((1/5I))((v_(h))/(2v_(h)))=2`
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