In a given semiconductor, the ratio of the number density of electron to number density of hole is 2: 1 . If 1 7 th of the total current is due to the hole and the remaining is due to the electrons, the ratio of the drift velocity of holes to the drift velocity of electrons is :

Step-by-step solution

Let n_e and n_h be the number densities of electrons and holes respectively. Given n_e n_h = 2 1 , so n_e = 2n_h . The total current I is the sum of electron current I_e and hole current I_h . Given I_h = 1 7 I , it follows that I_e = I - I_h = 6 7 I . The current is given by I = nqvA , where n is number density, q is charge magnitude, v is drift velocity, and A is cross-sectional area. Thus, I_e = n_e e v_e A and I_h = n_h e v_h A . Taking the ratio of I_h to I_e : I_h I_e = n_h e v_h A n_e e v_e A = n_h v_h n_e v