High Drift Velocities in Silicon vs Metals: Explained

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Drift velocities of electrons in silicon are higher than in metals due to the lower density of charge carriers in silicon, which allows for greater mobility of electrons when the same current flows. In metals, a higher number of charge carriers leads to increased scattering and lower drift velocities. The relationship between charge carrier density and drift velocity is crucial, as fewer carriers in silicon result in less resistance to motion. Additionally, the band structure of silicon allows for higher energy states, contributing to increased electron mobility. Understanding these factors clarifies the differences in drift velocities between these materials.
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Homework Statement


Explain why the drift velocity of electrons in silicon are relatively high when compared to drift velocities of electrons in metals of the same size, when the same current flows through both.

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The Attempt at a Solution


I stated that the number of charge carrier per unit volume in the case of conductors is n=1028m-3 and the one for the semi-conductor is n=1016m-3.
 
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... OK. So how is that related to the drift velocity?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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