An Electron's Wavelength

solved MatterWaves

Q. An electron of mass 9.11 × 10⁻³¹ kg $m = 9.11 \times 10^{−31}$ kg moves with a speed of 5.4 × 10⁶ m/s $v = 5.4 \times 10^{6}$ m/s. What is the de Broglie wavelength associated with it, in nm?

Inputs

mass

m

9.11e-31 kg

speed

v

5400000.0 m/s

Outputs

wavelength

λ

How it's solved

Solved with MatterWaves

Given

$m = 9.11 \times 10^{−31}$ kg
$v = 5.4 \times 10^{6}$ m/s

Find $λ$ .

Working

de broglie relation(electron) $λ = \frac{h}{m \cdot v}$
$λ = \frac{6.62607015 \times 10^{−34}}{9.11 \times 10^{−31} \cdot 5.4 \times 10^{6}}$
$λ = 0.1347$ nm
$λ = 1.34692648 \times 10^{−10}$ m $= 0.134692648$ nm
$λ \approx 0.135$ nmto 3 significant figures

Conclusion

A moving particle has a wavelength of Planck's constant over its momentum; the electron's is about an atom across.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :an_electron_s_wavelength do4  kind :numerical5  describes "An electron of mass %{mass} moves with a speed of %{speed}. %{wavelength}, in nm?"6  given mass: "9.11e-31 kg"7  given speed: "5.4e6 m/s"8  asks wavelength: "What is the de Broglie wavelength associated with it"9end

solution.rb

1require_relative "../questions/an_electron_s_wavelength"2require_relative "../science/dual_nature_of_radiation_and_matter/matter_waves"34solve :an_electron_s_wavelength, using: MatterWaves do5  objects :electron67  take mass: electron.mass8  take speed: electron.speed910  wavelength = electron.de_broglie_wavelength11  answer wavelength:, in: "nm", figures: 31213  conclusion "A moving particle has a wavelength of Planck's constant over its momentum; the electron's is " \14             "about an atom across."15end

playground.rb

1require_relative "../solutions/an_electron_s_wavelength"23play_with :an_electron_s_wavelength do4  title "An Electron's Wavelength"5end

The laws it drew on

quantity	written	units	within	from
plancks constant	$h$	J s	—	MatterWaves
mass	$m$	kg	0 … ∞	MatterWaves
speed	$v$	m/s	—	MatterWaves
de broglie wavelength	$λ$	m	—	MatterWaves
de broglie wavelength of ground	$λ_{g}$	m	—
mass of ground	$m_{g}$	kg	0 … ∞
speed of ground	$v_{g}$	m/s	—
de broglie wavelength of electron	$λ$	m	—
mass of electron	$m$	kg	0 … ∞
speed of electron	$v$	m/s	—

λ_{p} = \frac{h}{m_{p} \cdot v_{p}}

de broglie relation

λ_{g} = \frac{h}{m_{g} \cdot v_{g}}

de broglie relation(ground)

λ = \frac{h}{m \cdot v}

de broglie relation(electron)