In: Physics

# What is the speed of an electron that has been accelerated from rest through a potential difference of 1050?

What is the speed of an electron that has been accelerated from rest through a potential difference of 1050?

## Solutions

##### Expert Solution

Applying the law of conservation of energy,

KE of electron = Potential energy

$$\frac{1}{2} m\left(v^{2}-u^{2}\right)=\mathrm{qV}$$

Where $$m=$$ mass of elcetron, $$u=$$ initial speed $$=0 m / s, v=$$ final speed,

$$\mathrm{q}=$$ charge on electron, $$\mathrm{V}=$$ Potential diference $$=1050$$

$$\mathrm{v}=\sqrt{\frac{2 \mathrm{qV}}{m}}$$

Plugging the values,

$$\mathrm{v}=\sqrt{\frac{2\left(1.6 \times 10^{-19}\right)(1050)}{9.1 \times 10^{-31}}}=\sqrt{369 \times 10^{12}}=19.21 \times 10^{6} \mathrm{~m} / \mathrm{s}$$

Velocity of electron $$=19.21 \times 10^{6} \mathrm{~m} / \mathrm{s}$$ approx.

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