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QJEEM22Phd2b3: JEE Main 2022 Physics - Class 12 JEEM22Phd2b3 Solution: A potential barrier of 0.4 V exists across a p-n junction. An…

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 ×\times 105 ms −- 1. The speed with which electron enters the p side will be x3×105{x \over 3} \times {10^5} ms −- 1 the value of x is _____________.

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

Step-by-Step Verified Solution

Conserving energy,

12mv2=12m(6×105)2−0.4 eV{1 \over 2}m{v^2} = {1 \over 2}m{(6 \times {10^5})^2} - 0.4\,eV

⇒v=(6×105)2−2×1.6×10−19×0.49×10−31\Rightarrow v = \sqrt {{{(6 \times {{10}^5})}^2} - {{2 \times 1.6 \times {{10}^{ - 19}} \times 0.4} \over {9 \times {{10}^{ - 31}}}}}

=36×1010−1.289×1012= \sqrt {36 \times {{10}^{10}} - {{1.28} \over 9} \times {{10}^{12}}}

⇒v=143×105\Rightarrow v = {{14} \over 3} \times {10^5} m/s

⇒x=14\Rightarrow x = 14

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