---
title: "Wavelength of electron accelerated by 100 V"
subject: "Electrical Engineering Material"
chapter: 1
key: "semester_3/electrical_engineering_material:electron-wavelength-100v"
source: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/electron-wavelength-100v
site: BCT Engineering
---

# Wavelength of electron accelerated by 100 V

Electrical Engineering Material · Chapter 1: Theory of Metals

- Asked in: 2070 Chaitra, 4 marks
- Video: [DE- BROGLIE  WAVELENGTH OF AN ELECTRON](https://www.youtube.com/watch?v=aqlmVGF0Qcs) — CLASSIC PHYSICS
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electrical_engineering_material/electron-wavelength-100v
- Whole chapter: https://www.bctengineer.com/md/semester_3/electrical_engineering_material/chapter-1

## Question

Find the wavelength of an electron accelerated by 100V.

## Short answer

Using de Broglie relation λ = h/√(2meV): for V=100V, λ = 1.23×10⁻¹⁰ m = 0.123 nm (1.23 Å). Alternatively, λ = 1.227/√V nm.

## Answer

An electron accelerated from rest through a potential difference $V$ gains kinetic energy $eV$. Its momentum is $p = \sqrt{2meV}$ and its de Broglie wavelength is $\lambda = h/p$.

**Given:** $V = 100$ V, $m = 9.1\times10^{-31}$ kg, $e = 1.6\times10^{-19}$ C, $h = 6.626\times10^{-34}$ J s.

#### Kinetic energy and momentum

$$
\begin{aligned}
KE &= eV = 1.6\times10^{-19}\times100 = 1.6\times10^{-17}\ \text{J} \\
p &= \sqrt{2m\,eV} = \sqrt{2\times9.1\times10^{-31}\times1.6\times10^{-17}} \\
&= 5.396\times10^{-24}\ \text{kg m s}^{-1}
\end{aligned}
$$

#### Wavelength

$$
\lambda = \frac{h}{p} = \frac{6.626\times10^{-34}}{5.396\times10^{-24}} = 1.228\times10^{-10}\ \text{m}
$$

**Answer:** $\lambda = 1.23\times10^{-10}$ m $= 0.123$ nm $= 1.23$ Å.

Shortcut: $\lambda = \dfrac{1.227}{\sqrt{V}}$ nm $= \dfrac{1.227}{10} = 0.1227$ nm. This wavelength is of the same order as the spacing of atoms in a crystal, so such electrons are diffracted by crystals (Davisson–Germer experiment).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What kinetic energy does an electron gain when accelerated from rest through V volts?
   A. eV
   B. e/V
   C. e V^2
   D. mV
   Answer: A. Work done by the field is eV, which becomes kinetic energy. (Key point: Kinetic energy gained)

2. Which expression gives the electron's momentum from the accelerating voltage?
   A. p = eV/m
   B. p = sqrt(2 m e V)
   C. p = 2 m e V
   D. p = sqrt(eV/2m)
   Answer: B. eV = p^2/2m gives p = sqrt(2meV). (Key point: Momentum)

3. What is the wavelength of an electron accelerated by 100 V?
   A. 1.23 nm
   B. 0.123 nm
   C. 12.3 nm
   D. 0.0123 nm
   Answer: B. lambda = h/p = 1.228e-10 m = 0.123 nm, or 1.227/sqrt(100) nm. (Key point: de Broglie wavelength result)

## Related in Electrical Engineering Material

- [Photoelectric effect: work function of sodium](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aphotoelectric-sodium-work-function) — Electrical Engineering Material, chapter 1, asked 2×
- [Si with 10¹⁵ Sb: carriers, resistance, Fermi level](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aantimony-1e15-resistance-fermi) — Electrical Engineering Material, chapter 6
- [Compensated semiconductor concentrations and conductivity](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Acompensated-conductivity) — Electrical Engineering Material, chapter 6

## Related in other subjects

- [Double-stub matching 110+j110 Ω on 100 Ω line](https://www.bctengineer.com/question.md?key=semester_7%2Frf_and_microwave_engineering%3Adouble-stub-110-j110) — RF and Microwave Engineering, chapter 2, asked 2×
- [Mass of particle from de Broglie ratio](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adebroglie-ratio-mass-of-particle) — Engineering Physics, chapter 10
- [Square-wave inverter RL load current up to 5th order](https://www.bctengineer.com/question.md?key=semester_7%2Fpower_electronics%3Ainverter-square-wave-rl-fifth-order) — Power Electronics, chapter 5, asked 2×
- [SCR half-wave rectifier numerical (200 V peak)](https://www.bctengineer.com/question.md?key=semester_4%2Fadvanced_electronics%3Ascr-hwr-1ma-200v) — Advanced Electronics, chapter 7