A Dust Particle's Wavelength

solved MatterWaves

Q. What is the de Broglie wavelength of a dust particle of mass 1.0 × 10⁻⁹ kg $m = 1.0 \times 10^{−9}$ kg drifting with a speed of 2.2 m/s $v = 2.2$ m/s, in m?

Inputs

mass

m

1e-09 kg

speed

v

2.2 m/s

Outputs

wavelength

λ

How it's solved

Solved with MatterWaves

Given

$m = 1.0 \times 10^{−9}$ kg
$v = 2.2$ m/s

Find $λ$ .

Working

de broglie relation(particle) $λ = \frac{h}{m \cdot v}$
$λ = \frac{6.62607015 \times 10^{−34}}{1 \times 10^{−9} \cdot 2.2}$
$λ = 3.012 \times 10^{−25}$ m
$λ \approx 3.01 \times 10^{−25}$ mto 3 significant figures

Conclusion

A speck of dust is still far too massive for its wavelength to come near the size of anything we could measure.

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 :a_dust_particle_s_wavelength do4  kind :numerical5  describes "%{wavelength} of a dust particle of mass %{mass} drifting with a speed of %{speed}, in m?"6  given mass: "1.0e-9 kg"7  given speed: "2.2 m/s"8  asks wavelength: "What is the de Broglie wavelength"9end

solution.rb

1require_relative "../questions/a_dust_particle_s_wavelength"2require_relative "../science/dual_nature_of_radiation_and_matter/matter_waves"34solve :a_dust_particle_s_wavelength, using: MatterWaves do5  objects :particle67  take mass: particle.mass8  take speed: particle.speed910  wavelength = particle.de_broglie_wavelength11  answer wavelength:, in: "m", figures: 31213  conclusion "A speck of dust is still far too massive for its wavelength to come near the size of anything we " \14             "could measure."15end

playground.rb

1require_relative "../solutions/a_dust_particle_s_wavelength"23play_with :a_dust_particle_s_wavelength do4  title "A Dust Particle'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 particle	$λ$	m	—
mass of particle	$m$	kg	0 … ∞
speed of particle	$v$	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(particle)