Question

The smallest atoms can themselves exhibit quantum-mechanical behavior. Calculate the de Broglie wavelength (in picometers) of a hydrogen atom traveling at 490 m/s. Express your answer using three significant figures.

Answer 1

810 pm

Step-by-step explanation:

Step 1: Given and required data

• Velocity of the atom (v): 490 m/s

• Mass of a hydrogen atom (m): 1.67 × 10⁻²⁷ kg

• Planck's constant (h): 6.63 × 10⁻³⁴ J.s

Step 2: Calculate the de Broglie wavelength of the hydrogen atom

We will use de Broglie's equation.

λ = h / m × v

λ = 6.63 × 10⁻³⁴ J.s / 1.67 × 10⁻²⁷ kg × 490 m/s = 8.10 × 10⁻¹⁰ m

Step 3: Convert 8.10 × 10⁻¹⁰ m to picometers

We will use the conversion factor 1 m = 10¹² pm.

8.10 × 10⁻¹⁰ m × 10¹² pm/1 m = 810 pm