Obtain the expression for the de Broglie wavelength of an electron accelerated from rest through a potential difference V. Find its value for V = 100 V.

1. 1 · Start with the relation. λ = h/p.
2. 2 · Bring in the energy. eV = ½mv² = p²/(2m), so p = √(2meV).
3. 3 · Write the result. λ = h/√(2meV).
4. 4 · Put in the constants. For V = 100 V: p = √(2 × 9.11 × 10⁻³¹ × 1.6 × 10⁻¹⁹ × 100) ≈ 5.40 × 10⁻²⁴ kg m/s.
5. 5 · Calculate. λ = h/p = (6.63 × 10⁻³⁴) ÷ (5.40 × 10⁻²⁴) m ≈ 1.23 × 10⁻¹⁰ m = 0.123 nm.
6. 6 · Real life. Electron microscopes use this very short wavelength.
7. 7 · Close in one line. So, a higher accelerating voltage gives a shorter wavelength.

Scoring tip: Substitute h, m and e with their units and give λ in m or nm. The shortcut 1.227/√V nm is not in your textbook; use it only to check.