An electron with speed = 2.54×10^7m/s is traveling parallel to an electric field of magnitude = 1.66×104 N/C.

How far will the electron travel before it stops?
How much time will elapse before it returns to its starting point?

To solve these questions, we need to use the equations of motion for an object under constant acceleration. In this case, the electron is moving parallel to an electric field, so it experiences a constant force that causes it to decelerate.

First, let's find the acceleration of the electron using Newton's second law: F = ma

Given:
- Speed of the electron (v) = 2.54 × 10^7 m/s
- Electric field magnitude (E) = 1.66 × 10^4 N/C
- Charge of an electron (q) = 1.6 × 10^-19 C (this is a known constant)

The force experienced by the electron can be calculated using the equation: F = qE

Substituting the values, we have:
F = (1.6 × 10^-19 C) × (1.66 × 10^4 N/C)

Now, using Newton's second law, F = ma, we can solve for acceleration (a):
(1.6 × 10^-19 C) × (1.66 × 10^4 N/C) = (9.1 × 10^-31 kg) × a

Simplifying the equation, we find:
a = (1.6 × 1.66 × 10^-19 × 10^4) / (9.1 × 10^-31) m/s^2

Now that we have the acceleration, let's solve the first question:

1. How far will the electron travel before it stops?

In order to calculate the distance traveled (d) before the electron stops, we need to know the initial velocity (u), which is not provided. However, we can assume that the electron started from rest and accelerated to the given speed.

Using the equation of motion: v^2 = u^2 + 2ad

Where:
- v is the final velocity (in this case, it is 0 since the electron stops)
- u is the initial velocity
- a is the acceleration
- d is the distance traveled

Substituting the known values:
(0)^2 = (2.54 × 10^7)^2 + 2(a)(d)

Simplifying, we find:
0 = (2.54 × 10^7)^2 + 2(a)(d)

Now we can solve for d:
d = -((2.54 × 10^7)^2) / (2a)

Substituting the value of a calculated earlier, we can find the distance traveled before the electron stops.

2. How much time will elapse before it returns to its starting point?

To find the time it takes for the electron to return to its starting point (t), we need to know the distance traveled (d) and the initial velocity (u). Since the distance traveled is not given, we won't be able to find the exact time.

However, we can make an approximation that the electron travels a distance equal to its initial speed of 2.54 × 10^7 m/s (assuming it started from rest). In that case, the time taken (t) can be calculated using the equation: t = d / u

Substituting the known values:
t = (2.54 × 10^7 m/s) / (2.54 × 10^7 m/s)

Simplifying, we find:
t = 1 second

Therefore, the approximate time it takes for the electron to return to its starting point is 1 second.

Please note that these calculations assume certain initial conditions and make approximations. It's always important to consider the specific context and any given parameters when solving physics problems.