Chapter 25: Q. 12 (page 709)

What is the speed of an electron that has been accelerated from rest through a potential difference of $1000 V$ ?

Short Answer

Expert verified

The electron speed is $1.87 \times 10^{7} m / s$ .

Step by step solution

Given information and concept

Potential difference, $V = 1000 V$

Mass of electron, $m_{e} = 9.1 \times 10^{- 31} kg$

Charge of electron, $q = - 1.6 \times 10^{- 19} C$

Formula used:

The following is the relationship between potential energy and potential difference:

$U = q Δ V$

Where,

$U$ is the potential energy

q is the charge of electron

$Δ V$ is the potential difference

Find the speed of electron

Calculate the electron's potential energy.

$U = q Δ V$

Insert the value in the above equation

$\begin{array}{rcl} U & = & - 1.6 \times 10^{- 19} \times (1000) \\ = & - 1.6 \times 10^{- 16} J \end{array}$

All potential energy is turned into kinetic energy according to energy conservation.

$K E_{initial} - K E_{final} = U \frac{1}{2} m_{e} v_{initial}^{2} - \frac{1}{2} m_{e} v_{final}^{2} = U$

Insert the required value in the above equation

$\frac{1}{2} \times 9.1 \times 10^{- 31} \times 0 - \frac{1}{2} \times 9.1 \times 10^{- 31} \times v^{2} = - 1.6 \times 10^{- 16} 0 - \frac{1}{2} \times 9.1 \times 10^{- 31} \times v^{2} = - 1.6 \times 10^{- 16} v = \sqrt{\frac{1.6 \times 10^{- 16}}{\frac{1}{2} \times 9.1 \times 10^{- 31}}} = 1.87 \times 10^{7} m / s$

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What is the speed of an electron that has been accelerated from rest through a potential difference of $1000 V$ ?

Short Answer

Step by step solution

Given information and concept

Find the speed of electron

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What is the speed of an electron that has been accelerated from rest through a potential difference of 1000V?

Short Answer

Step by step solution

Given information and concept

Find the speed of electron

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Electromagnetism

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Study anywhere. Anytime. Across all devices.

What is the speed of an electron that has been accelerated from rest through a potential difference of $1000 V$ ?