Question

An electron is moving in a straight line with a velocity of 4.0×10⁵ m/s. It enters a region 5.0 cm long where it undergoes an acceleration of 6.0×10¹²m/s² along the same straight line. (a) What is the electron’s velocity when it emerges from this region?

a) 4.0×10⁵ m/s
b) 8.33×10⁻⁸ s
c) 2.0×10⁵ m/s
d) 2.5×10⁻⁸ s

Answer 1

The electron's velocity after passing through the acceleration region is approximately 4.0774 × 10⁵ m/s, having undergone an acceleration for about 1.29 × 10⁻⁸ s.

Step-by-step explanation:

To determine the electron's velocity after accelerating through the region, we can use the basic kinematic equation:

v = u + at

where:

• v is the final velocity
• u is the initial velocity (4.0 × 10⁵ m/s)
• a is the acceleration (6.0 × 10¹² m/s²)
• t is the time taken to cross the region

To find t, we need to know the length of the region and the electron's acceleration:

t = √(2d/a), where d is the distance (5.0 cm or 0.05 m).

Using the provided values:

t = √(2 × 0.05 m / 6.0 × 10¹² m/s²)
t ≈ 1.29 × 10⁻⁸ s

Now, plug this time into the first equation to find v:

v = 4.0 × 10⁵ m/s + (6.0 × 10¹² m/s²)(1.29 × 10⁻⁸ s)
v ≈ 4.0 × 10⁵ m/s + 774 m/s ≈ 4.0774 × 10⁵ m/s

The electron's velocity when it emerges from this region is approximately 4.0774 × 10⁵ m/s.