A Bullet's Wavelength

solved MatterWaves

Q. What is the de Broglie wavelength of a bullet of mass 0.040 kg $m = 0.040$ kg travelling at the speed of 1.0 km/s $v = 1.0$ km/s, in m?

Inputs

mass

m

0.04 kg

speed

v

1 km/s

Outputs

wavelength

λ

How it's solved

Solved with MatterWaves

Given

$m = 0.040$ kg
$v = 1.0$ km/s

Find $λ$ .

Working

$v = 1.0$ km/s $= 1000$ m/s
de broglie relation(particle) $λ = \frac{h}{m \cdot v}$
$λ = \frac{6.62607015 \times 10^{−34}}{0.04 \cdot 1000}$
$λ = 1.657 \times 10^{−35}$ m
$λ \approx 1.66 \times 10^{−35}$ mto 3 significant figures

Conclusion

A bullet's momentum is enormous next to Planck's constant, so its wavelength is far too small to show any wave behaviour.

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_bullet_s_wavelength do4  kind :numerical5  describes "%{wavelength} of a bullet of mass %{mass} travelling at the speed of %{speed}, in m?"6  given mass: "0.040 kg"7  given speed: "1.0 km/s"8  asks wavelength: "What is the de Broglie wavelength"9end

solution.rb

1require_relative "../questions/a_bullet_s_wavelength"2require_relative "../science/dual_nature_of_radiation_and_matter/matter_waves"34solve :a_bullet_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 bullet's momentum is enormous next to Planck's constant, so its wavelength is far too small to " \14             "show any wave behaviour."15end

playground.rb

1require_relative "../solutions/a_bullet_s_wavelength"23play_with :a_bullet_s_wavelength do4  title "A Bullet'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)