Question

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

• A. $4.6\times {10}^{7}m/s$
• B. $0.726\times {10}^{7}m/s$
• C. $0.23\times {10}^{2}m/s$
• D. $5.1\times {10}^{9}m/s$

Answer 1

Answer: (B)

V = 1500 V

u = 0, initial K.E = 0

Energy last by electron = $V.e=1500\times 1.602\times {10}^{-19}$

$\Rightarrow 2.403\times {10}^{-19}joules$

$\begin{array}{c}massofelectrons\left(m\right)=9.1\times {10}^{-31}kg\\ kineticenergygained=P.Elost\\ \frac{1}{2}m{V}^2=2.403\times {10}^{-17}\\ V^2=\frac{2\times 2.403\times {10}^{-17}}{9.1\times {10}^{-31}}=\frac{4.806\times {10}^{+14}}{9.1}=0.528\times {10}^{14}\\ V^2\sqrt{0.528\times {10}^{14}}=0.726\times {10}^{7}m/s\end{array}$