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The average speed of a diatomic fluorine molecule at 25 ∘C is 442.4 m⋅s−1 . What is the average wavelength of a fluorine molecule at this temperature? Assume that the molecule acts as a single particle

Sagot :

The average wavelength of the fluorine molecule will be 2.36 × 10⁻¹¹ metres.

Fluorine Molecule's Speed = 442.4 m/s

The Molar Mass of the F₂ = 38 g/mol

Now as we know that any molecule's

1 mole contain  = 6.022 × 10²³ Molecule

So, 1 Fluorine molecule mass =

Fluorine's Molar mass / Number of Fluorine molecule in 1 mole

So, 1 Fluorine molecule mass = 38 / ( 6.022 × 10²³ )

1 Fluorine molecule mass = 6.31 × 10⁻²³ g

1 Fluorine molecule mass = 6.31 × 10⁻²⁶  Kg

So molecule's momentum = Molecule's mass × Molecule's Velocity

So molecule's momentum = ( 6.31 × 10⁻²⁶ ) × 442.4

So molecule's momentum = 2.8 × 10⁻²³  Kg.m/s

Now wavelength of Fluorine molecule = λ = planks constant / momentum

wavelength of Fluorine molecule = λ = ( 6.626 × 10⁻³⁴ ) / ( 2.8 × 10⁻²³ )

wavelength of Fluorine molecule = λ = 2.36 × 10⁻¹¹ metre

So the wavelength of the diatomic fluorine molecule came out to be 2.36 × 10⁻¹¹ metres after applying all the concepts and formulas.

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