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faltersainse [42]
2 years ago
12

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.
Chemistry
1 answer:
Sunny_sXe [5.5K]2 years ago
5 0

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

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