A beam of electrons is accelerated through a potential difference of $150\ \text{V}$ . The electrons then pass through a narrow slit producing a diffraction pattern on a screen.

(a)

the de Broglie wavelength of the electrons. (Electron mass $m_e = 9.11 \times 10^{-31}\ \text{kg}$ , charge , Planck constant .)

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9.11×

10−31 kg

e=1.60 \times 10^{-19}\ \text{C}

h=6.63 \times 10^{-34}\ \text{J s}

[3]

(b)

why the observation of diffraction patterns from electrons demonstrates wave–particle duality.

[2]

(c)

how increasing the accelerating voltage affects the diffraction pattern.

[1]

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Double-slit experiment

Blackbody radiation

Photoelectric effect

Electron diffraction

Electrons are emitted with greater energy

No electrons are emitted

Current increases linearly

Electrons are emitted after a delay

Wavelength

Frequency

Amplitude

Intensity