Chapter 37: Q. 17 (page 1082)

Express in $e V$ (or $k e V$ or $M e V$ if more appropriate):
a. The kinetic energy of an electron moving with a speed of $5.0 \times 10^{6} m / s$ .
b. The potential energy of an electron and a proton $0.10 n m$ apart.
c. The kinetic energy of a proton that has accelerated from rest through a potential difference of $5000 V$ .

Short Answer

Expert verified

a. The kinetic energy of an electron is $E_{k} = 71.17 e V$

b. The potential energy of an electron and a proton $0.10 n m$ apart is $U = - 14.42 e V$ .

c. The kinetic energy of a proton is $E_{k} = 5 k e V$ .

Step by step solution

Part (a) step 1: Given information

We have given that the express in $e V$ .

We need to find kinetic energy of an electron moving with a speed of $5.0 \times 10^{6} m / s$ .

Part (a) step 2: Simplify

The expression for kinetic energy

$E_{k} = \frac{1}{2} m v^{2} E_{k} = \frac{1}{2} (9.11) (10^{- 31}) (5 {(10^{6}))}^{2} E_{k} = 1.13875 (10^{- 17}) J$

Part (b) step 1: Given information

We have given that the express in $e V$

We need to find potential energy of an electron and a proton $0.10 n m$ apart.

Part (b) step 2: Simplify

Using formula for potential energy :

$U = \frac{q_{1} q_{2}}{4 π \in_{0} r} U = \frac{e (- e)}{4 π \in_{0} (0.1) (10^{- 9})} U = - 2.307 (10^{- 18}) J = - 14.42 e V$

Part (c) step 1: Given information

We have given that the express in $e V$

We need to find the kinetic energy of a proton that has accelerated from rest through a potential difference of $5000 V$ .

Part (c) step 2: Simplify

The expression for kinetic energy when charge accelerating with a potential difference $∆ V$ :

$E_{k} = q ∆ V E_{k} = e ∆ V E_{k} = e (5000) E_{k} = 5 k e V$

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Short Answer

Step by step solution

Part (a) step 1: Given information

Part (a) step 2: Simplify

Part (b) step 1: Given information

Part (b) step 2: Simplify

Part (c) step 1: Given information

Part (c) step 2: Simplify

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Express in eV(or keVor MeVif more appropriate):a. The kinetic energy of an electron moving with a speed of 5.0×106m/s.b. The potential energy of an electron and a proton 0.10nmapart.c. The kinetic energy of a proton that has accelerated from rest through a potential difference of 5000V.

Short Answer

Step by step solution

Part (a) step 1: Given information

Part (a) step 2: Simplify

Part (b) step 1: Given information

Part (b) step 2: Simplify

Part (c) step 1: Given information

Part (c) step 2: Simplify

One App. One Place for Learning.

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