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Chapter 16: 21P (page 626)

If the kinetic energy of an electron is $4.4 脳 10^{- 18} J$ , what is the speed of the electron? You can use the approximate (non relativistic) equation here.

Short Answer

Expert verified

The speed of the electron is $3.11 脳 10^{6} m / s$
.

Step by step solution

01

Identification of the given data

The given data can be listed below as,

The kinetic energy of an electron is, $K E = 4.4 脳 10^{- 18} J$ .

02

Significance of kinetic energy

In this problem, the concept of a non-relativistic equation of kinetic energy will be used in order to estimate an electron's speed. The relation between the electron鈥檚 kinetic energy and electron mass is direct linear.

03

Determination the speed of an electron

The relation of kinetic energy of an electron is expressed as,

$K E = \frac{1}{2} m_{e} v^{2}$

Here, $m_{e}$ is the mass of an electron whose value is $9.1 脳 10^{- 31} k g$ and $v$ is the speed of the electron.

Substitute all the known values in the above equation.

$4.4 脳 10^{- 18} J = \frac{1}{2} 脳 (9.1 脳 10^{- 31} k g) 脳 v^{2} v^{2} = [\frac{2 (4.4 脳 10^{- 18} J)}{9.1 脳 10^{- 31} k g}] 鈮� (9.67032 脳 10^{12} J / k g) [\frac{1 m^{2} / s^{2}}{1 J / k g}] v 鈮� 3.11 脳 10^{6} m / s$

Thus, the speed of the electron is $3.11 脳 10^{6} m / s$ .

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Most popular questions from this chapter

An electron starts from rest in a vacuum, in a region of strong field. The electron moves through a potential difference of 44V. (a) What is the kinetic energy of the electron in electron volts (eV)? (b) Which of the following statements would be true if the particle were a proton? Choose both if they are both correct. (1) The kinetic energy of the proton would be negative. (2) The proton would move in the opposite direction from the electron.

You travel along a path from location A to location B, moving in the same direction as the direction of the net electric field in that region. What is true of the potential difference $V_{B} - V_{A}$ ? (1) $V_{B} - V_{A} > 0$ , (2) $V_{B} - V_{A} < 0$ , (3) $V_{B} - V_{A} = 0$ .

Question: In Chapter 6 we saw that the electric potential energy of a system of two particles is given by the equation $U_{e l} = \frac{1}{4 {蟺蔚}_{0}} \frac{q_{1} q_{2}}{r}$ .

(a) What is the electric potential energy of two protons separated by a distance of $9 nm (9 脳 10^{- 9} m)$ ? (b) What is the electric potential energy of a proton and an electron separated by the same distance?

You move from location i at $鉄� 2, 5, 4 鉄� 鈥� m$ to location f at $鉄� 3, 5, 9 鉄� 鈥� m$ . All along this path there is a nearby uniform electric field whose value is $鉄� 1000, 200, - 500 鉄� 鈥� N / C .$ . Calculate, $螖痴 = V_{f} - V_{i}$ including signs and units.

As shown in Figure 16.72, three large, thin, uniformly charged plates are arranged so that there are two adjacent regions of uniform electric field. The origin is at the center of the central plate. Location A is $< - 0.4, 0, 0 > m$ , and location B is $< 0.2, 0, 0 > m$ . The electric field $\overset{鈫�}{E_{1}}$ has the value $< 725, 0, 0 > V / m$ , and $\overset{鈫�}{E_{2}}$ is $< - 425, 0, 0 > V / m$ .

(d) What is the minimum kinetic energy the electron must have at location A in order to ensure that it reaches location B?

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