A Physicists often use a different unit of energy, the electron volt, when dealing wth e electron volt, abbreviated eV, is defined as the amount of kinetic energy gained by an electron upon accelerating through a 1.0 V potential difference. What is 1.0 electron volt in joules? at the atomic level. What is the speed of a proton with 2500 eV of kinetic energy? Express your answer with the appropriate units.

1ev = 1.609*10^-19 J

velocity of electron = v = 2.97 * 10^7 m/s

Explanation: The magnitude of an electronic charge (e) is given as

e = 1.609*10^-19c

The amount of kinetic energy an electron has when it moves through 1v equals the work done used in accelerating the electron ( according to work- energy theorem).

K.E = W = eV

e = magnitude of electron = 1.609 * 10^-19c

V = 1v

Hence 1ev = 1.609 * 10^-19 * 1

1ev = 1.609 * 10^-19 J.

If K.E = 2500ev.

By converting this to joules we have that

If 1ev = 1.609 * 10^-19 J.

Then 2500ev = 1.609 * 10^-19 * 2500

K.E ( in joules) = 4005 * 10^-19

K.E = 4.005 * 10^-16 J.

But K.E = 1/2mv²

Where K.E = kinetic energy of electron = 4.005 * 10^-16 J.

m = mass of electronic charge = 9.11 * 10 ^-31kg.

By substituting the parameters, we have that

4.005 * 10^-16 = 1/2 * 9.11 * 10 ^-31 * v²

4.005 * 10^-16 * 2 = 9.11 * 10 ^-31 * v²

8.01 * 10^-16 = 9.11 * 10^-31 * v²

v² = 8.01 * 10^-16/ 9.11 * 10^-31

v² = 0.879 * 10^15

v² = 8.79 * 10^14

v = √8.79 * 10^14

v = 2.97 * 10^7 m/s

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