---
title: "Mass of particle from de Broglie ratio"
subject: "Engineering Physics"
chapter: 10
key: "semester_1/engineering_physics:debroglie-ratio-mass-of-particle"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/debroglie-ratio-mass-of-particle
site: BCT Engineering
---

# Mass of particle from de Broglie ratio

Engineering Physics · Chapter 10: Photon and Matter Waves

- Asked in: 2074 Asoj, 5 marks
- Video: [A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the](https://www.youtube.com/watch?v=otJ0yhVFSvw) — physics spc sandeep sir
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/debroglie-ratio-mass-of-particle
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-10

## Question

A non relativistic particle is moving three times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.813 × 10⁻⁴. Calculate the mass of the particle.

## Short answer

From λ = h/(mv), λ_p/λ_e = (m_e v_e)/(m_p v_p). With v_p = 3v_e, m_p = m_e/(3 × ratio) = 9.109×10⁻³¹/(3×1.813×10⁻⁴) ≈ 1.675×10⁻²⁷ kg.

## Answer

de Broglie wavelength: λ = h/(mv). For the particle and the electron:

λ_p/λ_e = (m_e v_e)/(m_p v_p)

**Given:** v_p = 3 v_e, λ_p/λ_e = 1.813×10⁻⁴, m_e = 9.109×10⁻³¹ kg.

```text
λ_p/λ_e = m_e v_e / (m × 3 v_e) = m_e / (3m)

m = m_e / (3 × λ_p/λ_e)
  = 9.109×10⁻³¹ / (3 × 1.813×10⁻⁴)
  = 9.109×10⁻³¹ / 5.439×10⁻⁴
  = 1.675×10⁻²⁷ kg
```

**Answer: m ≈ 1.675×10⁻²⁷ kg**, which is the mass of a neutron (about 1839 m_e).

## Check yourself

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

1. The de Broglie wavelength is:
   A. λ = hmv
   B. λ = mv/h
   C. λ = h/(mv)
   D. λ = h/(mv²)
   Answer: C. λ is Planck's constant divided by momentum. (Key point: de Broglie wavelength)

2. With v_p = 3v_e, the ratio λ_p/λ_e equals:
   A. 3m_e/m
   B. m/(3m_e)
   C. 3m/m_e
   D. m_e/(3m)
   Answer: D. Heavier or faster particles have shorter wavelength, so the ratio is m_e v_e/(m 3v_e). (Key point: Ratio)

3. The mass of the particle is about:
   A. 1.675×10⁻²⁷ kg
   B. 5.5×10⁻³⁴ kg
   C. 3.0×10⁻²⁷ kg
   D. 1.675×10⁻²⁴ kg
   Answer: A. m = 9.109×10⁻³¹/(3 × 1.813×10⁻⁴) = 1.675×10⁻²⁷ kg, a neutron. (Key point: Final mass)

## Related in Engineering Physics

- [Cyclotron protons, charge-to-mass ratio](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Acyclotron-protons-charge-mass-ratio) — Engineering Physics, chapter 8
- [Energy of particle in infinite well](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Aparticle-infinite-well-energy-eigenvalue) — Engineering Physics, chapter 10, asked 7×
- [Conductivity of sodium from electron density](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Asodium-conductivity-electron-density) — Engineering Physics, chapter 8, asked 2×
- [Electron on ring axis performs SHM](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Aring-electron-shm-axial) — Engineering Physics, chapter 7
- [Displacement current density, dE/dt, induced B](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Adisplacement-current-density-dedt-plates) — Engineering Physics, chapter 9
- [Slope of string equals speed ratio](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Astring-wave-slope-speed-ratio) — Engineering Physics, chapter 2

## Related in other subjects

- [Wavelength of electron accelerated by 100 V](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Aelectron-wavelength-100v) — Electrical Engineering Material, chapter 1
- [Effective mass of electron in gold](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Agold-effective-mass-justify) — Electrical Engineering Material, chapter 1
- [Velocity and acceleration of moving particle at t=1](https://www.bctengineer.com/question.md?key=semester_2%2Fmathematics%3Avelocity-acceleration-moving-particle-t) — Mathematics, chapter 5
- [Effective mass of a free electron](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Afree-electron-effective-mass) — Electrical Engineering Material, chapter 1, asked 3×