an electron is accelerated from rest to a speed of 2.0 x 10^6 meter per second. how much kinetic energy is gained by the electron as it is accelerated from rest to this speed

Respuesta :

Answer:

Approximately [tex]1.8 \times 10^{-18}\; {\rm J}[/tex].

Explanation:

Since the speed of this electron is significantly lower than the speed of light (around [tex]0.015[/tex],) the kinetic energy of this electron can be approximated with the equation:

[tex]\displaystyle (\text{KE}) = \frac{1}{2}\, m\, v^{2}[/tex],

Where:

  • [tex]m \approx 9.109 \times 10^{-31}\; {\rm kg}[/tex] is mass of a stationary electron, and
  • [tex]v = 2.0 \times 10^{6}\; {\rm m\cdot s^{-1}}[/tex] is the velocity of this electron.

Substitute in the values and evaluate to obtain:

[tex]\begin{aligned} (\text{KE}) &= \frac{1}{2}\, m\, v^{2} \\ &\approx \frac{1}{2}\, \left(9.109 \times 10^{-31}\; {\rm kg})\, (2.0 \times 10^{6}\; {\rm m\cdot s^{-1}})^{2} \\ &\approx 1.82 \times 10^{-18}\; {\rm J}\end{aligned}[/tex].

In other words, the kinetic energy of this electron would be approximately [tex]1.82 \times 10^{-18}\; {\rm J}[/tex].