Question

An electron is to be accelerated in a uniform electric field having a strength of 2×10⁶ V/m. What energy in keV is given to the electron if it is accelerated through 24.8 cm ?

Answer 1

To find the energy in keV given to an electron accelerated through an electric field, multiply the field strength by the electron's charge and the distance traveled. The electron gains roughly 0.496 keV of energy when accelerated through 24.8 cm in a 2×106 V/m electric field.

Step-by-step explanation:

The question pertains to the acceleration of an electron through a uniform electric field and the consequent energy gain by the electron. We can calculate the energy given to the electron by using the formula Energy (E) = Electric Field (E) × Charge of electron (e) × Distance (d). Given the electric field strength (2×106 V/m), the charge of an electron (1.60×10-19 C), and the distance through which the electron is accelerated (24.8 cm), we proceed as follows:

First, the distance needs to be converted from centimeters to meters: 24.8 cm = 0.248 m. Now, compute the energy gained by the electron in joules: E = E × e × d = 2×106 V/m × 1.60×10-19 C × 0.248 m = 7.936×10-14 J. To convert joules to kilo-electronvolts (keV), we use the conversion factor 1 eV = 1.602×10-19 J and find that: 7.936×10-14 J × (1 eV / 1.602×10-19 J) × (1 keV / 1000 eV) ≈ 0.496 keV. Thus, the electron gains approximately 0.496 keV of energy.

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