Question

calculate the de-broglie wavelength of a molecule of co2 having a kinetic energy of 4x10 raised power -8?

Answer 1

mass of one molecule of CO₂ , m= 44/6.023 × 10²³ [ mass of one molecule of A= mass of one mole of A × Avogadro's constant ]
Given, kinetic energy , K.E = 4 × 10⁻⁸ J
we know, K.E = P²/2m
Here, P is momentum of molecule and m is the mass of molecule
so, P = √{2K.Em} --------(1)

Now, according to De- broglie's wavelength formula
λ = h/P
= h/√{2K.Em} [ from equation (1) ]
Here, h = 6.62 × 10⁻³⁴Js , m = 44/6.023 × 10²³ g = {44/6.023} × 10⁻²⁶ Kg
K.E = 4 × 10⁻⁸ J
so, λ = 6.62 × 10⁻³⁴/√{2 × 4 × 10⁻⁸ × ( 44/6.023)× 10⁻²⁶ }
= 6.62 × 10⁻³⁴⁺¹⁷/√{352/6.023}
= 6.62 × 10⁻¹⁷/7.64
= 0.866 × 10⁻¹⁷ m

Hence, wavelength of a molecule of CO₂ is 8.66 × 10⁻¹⁸m