JEE MAIN - Physics (2022 - 29th June Evening Shift - No. 23)
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 $${x \over 3} \times {10^5}$$ 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.)
Explanation
Conserving energy,
$${1 \over 2}m{v^2} = {1 \over 2}m{(6 \times {10^5})^2} - 0.4\,eV$$
$$ \Rightarrow v = \sqrt {{{(6 \times {{10}^5})}^2} - {{2 \times 1.6 \times {{10}^{ - 19}} \times 0.4} \over {9 \times {{10}^{ - 31}}}}} $$
$$ = \sqrt {36 \times {{10}^{10}} - {{1.28} \over 9} \times {{10}^{12}}} $$
$$ \Rightarrow v = {{14} \over 3} \times {10^5}$$ m/s
$$ \Rightarrow x = 14$$
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