Achieve HW #17

[Lizbeth Crisanto 3D]

I'm having trouble trying to solve #17 which states "The average speed of a diatomic chlorine molecule at 25 ∘C is 323.9 m⋅s−1 . What is the average wavelength of a chlorine molecule at this temperature? Assume that the molecule acts as a single particle." I first divided the molar mass by Avogadro’s constant, and multiplied by two, which got me 1.18*10^-25 and then I used de Broglie's equation and plugged in my previous answer into this equation and got 6.16*10^11, but it says its wrong. Am I missing something? And what are we supposed to do with the 25 C? Thanks in advance!

[Jessica Cornelia Hongarta 1G]

Hey! So, I believe the steps you did is already correct. However, I obtained a different answer from yours so I think it may have just been a miscalculation? Here's my work:

1. Find mass of the diatomic chlorine molecule → mass of Cl2 molecule = (2 × 35.45)/(6.0221 × 10^23) = 1.18 × 10^-22 g = 1.18 × 10^-25 kg
2. Plug the mass and velocity into the De Broglie equation → λ = h/mv → λ = (6.626 × 10^-34)/(1.18 × 10^-25 × 323.9) → λ = 1.74 × 10^-11 m

I don't know if this is the right answer but hopefully this helps!