Question

If the ratio of the concentration of electrons to that of holes in a semiconductor is $\frac{7}{5}$ and the ratio of current is $\frac{7}{4},$ then the ratio of their drift velocities is $\frac{N}{8}.$ The value of $N$(integer only)

Answer 1

Given, $\frac{n_e}{n_h}=\frac{7}{5};\frac{I_e}{I_h}=\frac{7}{4}$

As we know, $I=neA{v}_d$

$\Rightarrow \frac{I_e}{I_h}=\frac{n_e\times (v_d{)}_e\times Ae}{n_h\times (v_d{)}_h\times Ae}$

$\Rightarrow \frac{7}{4}=\frac{7}{5}\times \frac{(v_d{)}_e}{(v_d{)}_h}$

$\Rightarrow \frac{(v_d{)}_e}{(v_d{)}_h}=\frac{5}{7}\times \frac{7}{4}=\frac{5}{4}=\frac{10}{8}$

$\therefore N=10$