An Electron's Wavelength

Q. An electron of mass 9.11 × 10⁻³¹ kg moves with a speed of 5.4 × 10⁶ m/s. What is the de Broglie wavelength associated with it, in nm? expects 0.135 nm

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The web of concepts

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The equations it used

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Check an answer

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?

The playground

Inputs

mass

m

9.11e-31 kg

speed

v

5400000.0 m/s

Outputs

wavelength

λ

The solution

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 Ruby

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

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

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

The laws

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)