Question

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 × 10⁵ ms^-1. The speed with which the electron enters the p side will be `x/3 xx 10^5 "ms"^-1`, and the value of x is ______.

(Given the mass of electron = 9 × 10^-31 kg, the charge on electron = 1.6 × 10^-19 C.)

विकल्प

• 10

• 11

• 12

• 14

Answer 1

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 × 10⁵ ms^-1. The speed with which the electron enters the p side will be `x/3 xx 10^5 "ms"^-1`, and the value of x is 14.

Explanation:

We have, using the Work-Energy theorem,

W = `K_"initial" - K_"final"`

`qV = 1/2mv_i^2 - 1/2mv_f^2`

`1.6 xx 10^-19 xx 0.4 = 1/2m[v_i^2 - v_f^2]`

`1.6 xx 10^-19 xx 0.4 = 1/2 xx 9 xx 10^-31 xx [36 xx 10^10 - x^2/9 xx 10^10]`

`1.6 xx 0.4 xx 10^-19 = 1/2 xx 9 xx 10^-31 xx 10^10 xx [36 - x^2/9]`

⇒ `[36 - x^2/9] = (1.6 xx 0.4 xx 10^-19 xx 2)/(9 xx 10^-31 xx 10^10)`

⇒ `(324 - x^2)/9 = (1.6 xx 0.4 xx 2 xx 10^2)/9`

⇒ 324 - x² = 128

⇒ x² = 196

x = ±14

As a result, x = 14 m/s, because speed cannot be negative.