Question

An electron falls through a distance h = 1.5 cm in a uniform electric field E = 2.0 × 10⁴ N C⁻¹. Using the formula \[t = \sqrt{\frac{2hm}{qE}}\] and the electron mass mₑ = 9.1 × 10⁻³¹ kg with charge q = 1.6 × 10⁻¹⁹ C, what is the approximate time of fall?

Options

• Approximately 1.5 × 10⁻² s

• Approximately 1.25 × 10⁻⁷ s

• Approximately 2.9 × 10⁻⁹ s

• Approximately 3.5 × 10¹⁵ s

Answer 1

Using the given formula \[t = \sqrt{\frac{2hm}{qE}}\], substituting the electron's values: \[t_e = \sqrt{\frac{2 \times 1.5 \times 10^{-2} \times 9.1 \times 10^{-31}}{1.6 \times 10^{-19} \times 2.0 \times 10^4}} \approx 2.9 \times 10^{-9}\text{ s}\]. This extremely short time reflects the enormous acceleration (~3.5 × 10¹⁵ m s⁻²) experienced by the electron due to the electric field, making gravitational effects completely negligible.