Final answer:
The work required to stop an electron with a mass of 9.11x10⁻³¹ kg moving at 1.90x10⁶ m/s is calculated using its kinetic energy and equals 1.64x10⁻¹¶ joules.
Step-by-step explanation:
The amount of work required to stop an electron moving at a certain speed can be calculated using the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. In this case, the electron is being brought to a stop, which means all its kinetic energy will be removed. The kinetic energy (KE) of an electron is given by the formula: KE = ½ mv², where m is the mass of the electron and v is its velocity.
For an electron (m=9.11×10⁻³¹ kg) moving with a speed of 1.90×10⁶ m/s, the kinetic energy (and thus the work required to stop it) is:
KE = ½ (9.11×10⁻³¹ kg) × (1.90×10⁶ m/s)²
KE = ½ × 9.11×10⁻³¹ kg × 3.61×10¹² m²/s²
KE = ½ × 9.11×10⁻³¹ kg × 3.61×10¹² m²/s²
= 1.64×10⁻¹¶ joules
The work done to stop the electron is equal to the kinetic energy which is 1.64×10⁻¹¶ joules.