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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 $1.87 脳 10^{7} m / s$ .

Step by step solution

01

Given information and concept

Potential difference, $V = 1000 V$

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

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

Formula used:

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

$U = q 螖 V$

Where,

$U$ is the potential energy

q is the charge of electron

$螖 V$ is the potential difference

02

Find the speed of electron

Calculate the electron's potential energy.

$U = q 螖 V$

Insert the value in the above equation

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

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

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

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Most popular questions from this chapter

A proton and an alpha particle $(q = + 2 e, m = 4 u)$ are fired directly toward each other from far away, each with an initial speed of $0.010 c$ . What is their distance of closest approach, as measured between their centers?

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A -10.0 nC point charge and a +20.0 nC point charge are 15.0 cm apart on the x-axis. a. What is the electric potential at the point on the x-axis where the electric field is zero? b. What is the magnitude of the electric field at the point on the x-axis, between the charges, where the electric potential is zero?

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One form of nuclear radiation, beta decay, occurs when a neutron changes into a proton, an electron, and a neutral particle called a neutrino: $n 鈫� p^{+} + e^{-} + v$ where $n$ is the symbol for a neutrino. When this change happens to a neutron within the nucleus of an atom, the proton remains behind in the nucleus while the electron and neutrino are ejected from the nucleus. The ejected electron is called a beta particle. One nucleus that exhibits beta decay is the isotope of hydrogen $3 H$ , called tritium, whose nucleus consists of one proton (making it hydrogen) and two neutrons (giving tritium an atomic mass $m = 3 u$ ). Tritium is radioactive, and it decays to helium: ${}^{3}H 鈫� {}^{3}H e + e^{-} + n$

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