Final answer:
The potential difference needed to stop an electron with an initial velocity of 8.0×10⁵ m/s can be found by equating its initial kinetic energy to the electric potential energy it will have when stopped. The potential difference (V) is calculated using V = ½mv²/q, with m as the mass of the electron and q as its charge.
Step-by-step explanation:
The question is asking what potential difference is needed to stop an electron with an initial velocity of 8.0×10⁵ m/s. To find this, we can use the concept of energy conservation, where the kinetic energy of the electron is converted into electrical potential energy when the electron is stopped. The kinetic energy (KE) of the electron initially can be calculated using the equation KE = ½mv², where m is the mass of the electron (9.11×10⁻³¹ kg) and v is its velocity. The electrical potential energy (U) that the electron will have is U = qV, where q is the charge of the electron (-1.60×10⁻¹⁹ C).
Since the electron is brought to a stop, the entire kinetic energy is converted into electric potential energy, thus we have KE = U:
½mv² = qV. We can solve this equation for V (potential difference):
V = ½mv²/q.
Substituting in the given values:
V = ½(9.11×10⁻³¹ kg)(8.0×10⁵ m/s)² / (-1.60×10⁻¹⁹ C).
Calculating this expression gives us the potential difference needed to stop the electron.