Question

An electron is to be accelerated in a uniform electric field having a strength of (2.00 times 10^6 V/m).

(a) What energy in keV is given to the electron if it is accelerated through 0.400 m?
A) (1.6 keV)
B) (3.2 keV)
C) (6.4 keV)
D) (12.8 keV)
Over what distance would it have to be accelerated to increase its energy by 50.0 GeV?
A) (0.025 m)
B) (0.050 m)
C) (0.100 m)
D) (0.200 m)

Answer 1

An electron accelerated in a uniform electric field can have its energy calculated using the formula Energy = charge x potential difference. By rearranging that formula, we can also determine the distance needed to increase the energy by a certain amount.

Step-by-step explanation:

To calculate the energy given to the electron, we can use the formula:

Energy = charge x potential difference

The charge of an electron is 1.6 x 10-19 C. The potential difference is given as 2.00 x 106 V/m multiplied by 0.400 m.

Plugging in the values, we get:

Energy = (1.6 x 10-19 C) x (2.00 x 106 V/m) x (0.400 m) = 1.28 x 10-13 J

Converting this to keV, we divide by 1.6 x 10-19 J/eV:

Energy = (1.28 x 10-13 J) / (1.6 x 10-19 J/eV) = 8.0 x 105 eV = 8 keV

To find the distance needed to increase the energy by 50.0 GeV, we can rearrange the formula and solve for distance:

Distance = Energy / (charge x potential difference)

Plugging in the values, we get:

Distance = (50.0 x 109 eV) / (1.6 x 10-19 C x 2.00 x 106 V/m) = 1.56 x 10-3 m = 0.00156 m

Therefore, the correct answer is (0.00156 m).