Electrons are caused to fall through a potential difference of 1500 volt. If they were initially at rest, their final speed is

4.6 \times 10^{7} m / s

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0.726 \times 10^{7} m / s

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0.23 \times 10^{2} m / s

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5.1 \times 10^{9} m / s

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Solution

The correct option is B $0.726 \times 10^{7} m / s$
V = 1500 V
u = 0, initial K.E = 0
Energy last by electron = $V . e = 1500 \times 1.602 \times 10^{- 19}$
$\Rightarrow 2.403 \times 10^{- 19} j o u l e s$
$\begin{matrix} m a s s o f e l e c t r o n s (m) = 9.1 \times 10^{- 31} k g k i n e t i c e n e r g y g a i n e d = P . E l o s t \frac{1}{2} m V^{2} = 2.403 \times 10^{- 17} V^{2} = \frac{2 \times 2.403 \times 10^{- 17}}{9.1 \times 10^{- 31}} = \frac{4.806 \times 10^{+ 14}}{9.1} = 0.528 \times 10^{14} V^{2} \sqrt{0.528 \times 10^{14}} = 0.726 \times 10^{7} m / s \end{matrix}$

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