An electron of mass 9.1x 10 ^ -31 kg is travelling at a speed of 2.0 x 10 ^6 ms ^ -1 . Calculate the associate…

Analyze the question: We need the de Broglie wavelength of an electron moving at a known speed.

Concept: Every moving particle has an associated wave with wavelength

λ = h / (mv)

where h is Planck's constant, m is the mass and v is the speed.

Solution:

1. Momentum: mv = (9.1 × 10⁻³¹ kg)(2.0 × 10⁶ m/s) = 18.2 × 10⁻²⁵ = 1.82 × 10⁻²⁴ kg m/s

2. Wavelength: λ = (6.6 × 10⁻³⁴) / (1.82 × 10⁻²⁴)

3. Divide the numbers: 6.6 / 1.82 ≈ 3.63

4. Divide the powers of ten: 10⁻³⁴ / 10⁻²⁴ = 10⁻¹⁰

λ ≈ 3.63 × 10⁻¹⁰ m

Tip: In de Broglie questions, combine the mass and speed first to get the momentum, then divide h by it. For ordinary electrons, the wavelength is usually around 10⁻¹⁰ m (atomic size), so options with 10⁻⁷ or 10⁻⁴ are quickly ruled out.