Answer:
810 pm
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
