Question

The average speed of a diatomic oxygen molecule at 25 ∘C is 482.1 m⋅s−1 . What is the average wavelength of an oxygen molecule at this temperature? Assume that the molecule acts as a single particle.

Answer 1

given

average speed of a diatomic oxygen molecule at 25 °C is 482.1 ms⁻¹

now

wavelength (λ)=h/mv

h is the Planck's constant

m is the mass

v is the speed

mass of oxygen molecule = ?

1 mole contains 6.023 * 10²³ molecules

So

One molecule contains (1/6.023 * 10²³) moles

molar Mass of oxygen molecule is 32 g/mol

Mass = (32 g/mol) * (1/6.023 * 10²³) moles

= 5.31 * 10^-23 g = 5.31 * 10^-26 kg

so

λ = h/mv

= (6.626 * 10^-34 m² kg / s) / (5.31 * 10^-26 kg*482.1 m/s)

= 2.588 * 10^-11 m

= 25.88 pm