به انگلیسی

When particles behave like waves

Science · Waves, Light & Sound · ages 17-18

Name ______________________ Date ____________

An electron's momentum doubles while h stays fixed. What happens to its wavelength?
- It doubles
- It halves
- It stays the same
Which observation proves that electrons behave as waves?
- Light casting sharp shadows
- Rings from electrons through graphite
- Echoes bouncing off a wall
A flying cricket ball has a wavelength far too tiny to ever show diffraction.
Circle one: True False
A 0.05 kg tennis ball moves at 20 m/s. Its de Broglie wavelength is about 6.6e-34 m, far too small to notice.
Circle one: True False
The accelerating voltage is raised from 100 V to 900 V. What happens to the electron's de Broglie wavelength?
- It falls to one third
- It falls to one ninth
- It grows three times
- It stays the same
An electron is accelerated from rest through 600 V. Take e = 1.6e-19 C, m = 9.11e-31 kg and h = 6.63e-34 J s. Find its de Broglie wavelength in units of 10^-11 m, to 2 significant figures.
Answer: ______________
Electrons diffract through graphite into rings. The voltage is raised. What happens to the rings?
- They grow wider
- They vanish at once
- They shrink inward
Electron diffraction rings from graphite shrink when the accelerating voltage is raised. Why?
- Electron waves get shorter and bend less
- The graphite crystal shrinks as it heats
- Fewer electrons reach the screen
- Slower electrons spread out less
Ben expects electron diffraction at a wide open doorway. Why will he see nothing?
- The gaps must be near atomic size
- Electrons move too slowly to diffract
- Crystals absorb every electron
The accelerating voltage drops to one quarter of its value. What happens to the wavelength?
- It doubles
- It halves
- It stays the same

Answer key

For grown-ups. Fold this page away before handing over the rest.

When particles behave like waves W1-mt_Y8NthsmPcv-s1

It halves · Wavelength is h over momentum, so twice the bottom means half the wavelength.
Rings from electrons through graphite · Diffraction rings need interfering waves, and the electrons draw them.
True · Its huge momentum makes its wavelength absurdly smaller than any object it meets.
True · Its momentum is 0.05 x 20 = 1.0 kg m/s, so its wavelength is 6.63e-34 / 1.0, about 6.6e-34 m. No gap is anywhere near that small.
It falls to one third · The voltage rises 9 times, momentum rises by the square root of 9, which is 3, so the wavelength falls to one third.
5 · E = 1.6e-19 x 600 = 9.6e-17 J, p = square root of (2 x 9.11e-31 x 9.6e-17), about 1.32e-23 kg m/s, so the wavelength is 6.63e-34 / 1.32e-23 = 5.0e-11 m.
They shrink inward · Higher voltage shortens the wavelength, and shorter waves bend through smaller angles.
Electron waves get shorter and bend less · A higher voltage gives more momentum and a shorter wavelength, and shorter waves bend through smaller angles, so the rings close in.
The gaps must be near atomic size · Electron wavelengths sit near 1e-10 m, so only atomic-scale gaps can reveal them.
It doubles · Momentum follows the square root of voltage, so quarter voltage halves momentum and doubles wavelength.