Sample
Voltage 3000 V
Quantum Classical
Reset
Measurement on the screen
Planes
Circle r0.0 mm
Record Clear data
Sample : —
Momentum p = √(2mqV): —
Electrons detected : 0
Radius read on the scale r: —
δ = arctan (r/L): —
λ = d · sin δ: —
p λ: —
V
r (mm)
δ (rad)
λ (pm)
pλ (10⁻³⁴)
Measurements recorded : 0
Mean of pλ: —
accepted value h = 6.626 · 10⁻³⁴ J·s · deviation —
How the measurement is made. The gun accelerates the electrons through the voltage V, so their momentum is p = √(2mqV): it is displayed above. The electrons reach the screen one at a time, as dots; after a few thousand arrivals the rings appear, which are the diffraction pattern of the crystal lattice. They are not thin lines: they are bands as wide as the direct beam spot, sitting on the diffuse background of the inelastic collisions, and you aim at the middle of the band. A large lattice spacing d goes with a small angle, so the first ring from the centre is the one of the largest d : pairing it with the wrong planes throws pλ off by 40 or 70 per cent. Choose which family of planes the ring belongs to, then bring the measuring circle onto it — a tap on the screen moves it there, the slider fine-tunes it — and read the radius r on the graduated scale, in millimetres. The screen is L = 135 mm from the sample, so δ = arctan(r/L). The diffraction condition sin δ = λ/d, with d known from the structure of the crystal, gives the wavelength λ. Record the measurement and repeat it at other voltages: the product pλ stays constant, and it is Planck's constant. The reading is rounded to the half millimetre, and that is where the spread of the pλ values comes from. The phosphors of the screen fade in about ten seconds, so after a while the figure stops growing: what you see is the rate of the arrivals, not their total. On pause it stays put, like a photograph. A polycrystalline sample (randomly oriented crystallites) gives rings; a single crystal gives a lattice of spots, a projection of the reciprocal lattice. The classical model would give only a central blob, and there would be nothing to measure.