Difference between revisions of "De Broglie Wavelength"

Revision as of 14:38, 23 May 2024

Key Stage 5

Meaning

The de Broglie wavelength is the wavelength associated with a particle (an object with mass) and is inversely proportional to its momentum, demonstrating the Wave-Particle Duality|wave-like nature]] of matter.

About de Broglie Wavelength

The de Broglie wavelength suggests that particles such as electrons have wave properties.
The de Broglie wavelength is confirmed by experiments such as electron diffraction through a crystal.
The de Broglie wavelength is fundamental to the development of quantum mechanics.
The de Broglie wavelength applies to all particles, including macroscopic objects, but the wavelength is significant only for very small particles like electrons.

Formula

The de Broglie Wavelength of an object is given by the formula:

\[\lambda = \frac {h} {𝑝}\]

\[\lambda = \frac {h} {mv}\]

Where:

𝜆 is the de Broglie wavelength,

ℎ is the Planck Constant,

𝑝 is the momentum of the object

m is the mass of the object

v is the velocity of the object

Examples

Electrons showing diffraction patterns when passing through a thin crystal.
The de Broglie wavelength of a moving car is extremely small and not observable.

@@ Line 1: / Line 1: @@
 ==Key Stage 5==
 ===Meaning===
-The [[de Broglie wavelength]] is the [[wavelength]] associated with a particle and is inversely proportional to its momentum, demonstrating the wave-like nature of matter.
+The '''de Broglie wavelength''' is the [[wavelength]] associated with a [[particle]] (an object with mass) and is [[Inversely Proportional|inversely proportional]] to its [[momentum]], demonstrating the Wave-Particle Duality|wave-like nature]] of [[matter]].
 ===About de Broglie Wavelength===
+*The '''de Broglie wavelength''' suggests that [[particle]]s such as [[electron]]s have [[wave]] properties.
+*The '''de Broglie wavelength''' is confirmed by experiments such as [[Electron Diffraction|electron diffraction]] through a crystal.
+*The '''de Broglie wavelength''' is fundamental to the development of [[Quantum Mechanics|quantum mechanics]].
+*The '''de Broglie wavelength''' applies to all [[particle]]s, including [[macroscopic]] [[objects]], but the [[wavelength]] is significant only for very small [[particle]]s like [[electron]]s.
+===Formula===
+The '''de Broglie Wavelength''' of an [[object]] is given by the formula:
+:<math>\lambda = \frac {h} {𝑝}</math>
+:<math>\lambda = \frac {h} {mv}</math>
-Given by the formula
-𝜆
-=
-ℎ
-𝑝
-λ=
-p
-h
-  , where
+Where:
-𝜆
-λ is the wavelength,
-ℎ
-h is the [[Planck constant]], and
-𝑝
-p is the momentum.
-Suggests that [[particle]]s such as [[electron]]s have [[wave]] properties.
-Confirmed by experiments such as electron diffraction through a crystal.
-Fundamental to the development of quantum mechanics.
-The concept applies to all particles, including macroscopic objects, but the [[wavelength]] is significant only for very small [[particle]]s like [[electron]]s.
-===Formula===
+𝜆 is the '''de Broglie''' [[wavelength]],
+ℎ is the [[Planck Constant]],
+𝑝 is the [[momentum]] of the [[object]]
-The '''de Broglie Wavelength''' of an [[object]] is given by the formula:
+m is the [[mass]] of the [[object]]
-:<math>~ \lambda = \frac {h} {mv}. </math>
+v is the [[velocity]] of the [[object]]
 ===Examples===
-Electrons showing diffraction patterns when passing through a thin crystal.
+*[[Electron]]s showing diffraction patterns when passing through a thin crystal.
-The de Broglie [[wavelength]] of a moving car is extremely small and not observable.
+*The '''de Broglie wavelength''' of a moving car is extremely small and not observable.