What is the de Broglie wavelength of an oxygen molecule, O2 traveling at 521 m/s? Is the wavelength much smaller or much larger than the diameter of an atom. (on the order of 100 pm)

Question

De Broglie wavelength = h/mv
h = Planck's constant in J*s.
m is mass in kg.
v is velocity in m/s

Okay for this one I did

6.63 X 10^-34 J*s/ (?kg) (6210 m/s)

I don't understand how I get the kg for the problem

Answer 1

sorry I copied the wrong problem it is supposed to be: 521 m/s not 6210 m/s
6.63 X 10^-34/ (? kg)(521 m/s)

How do I get the kg for this problem

Answer 2

1 mol O2 has a mass of 32 g and contains 6.02 x 10^23 molecules OR 2 x 6.02 x 10^23 atoms. Therefore, 1 atom of oxygen has a mass of ???

Answer 3

3.01 x 10^23 ???

Answer 4

Let's see now. Do you have any idea how large a number 3.01 x 10^23 grams is? Do you think 1 single atom of oxygen can weigh
600,000,000,000,000,000,000,000 grams. That's one heavy atom.

Answer 5

yes I know how big that is but I figured that you had 2 atoms of 6.02 x 10^23 so I divided by 2 to get the mass of 1 mol which is 3.01 X 10^23...

why wouldnt you just take the 100 pm and make it into kg.

Answer 6

Aha!. I wondered how you did it. But you KNOW 1 atom of oxygen can't possibly weigh that much. You can't even see 1 atom of oxygen so you know the mass of 1 atom must be very small. And your number isn't very small; it is very large. The mass of 1 mol is 32 grams. I told you that in my first response.
1 mol (not 1 molecule) has a mass of 32 grams and contains 12.04 x 10^23 atoms of oxygen. So 1 atom must have a mass of
(32 g/mol) x (1 mol/12.04 x 10^23 atoms) = ?? grams/1 atom.

Answer 7

so that equals 2.66 grams/ 1 atom

now where do I go from there

Answer 8

Absolutely not!
32/12.04 x 10^23 = WHAT. You dropped the exponent again.
My calculator gives me 2.66 x 10^-23 grams.
What next? Change this to kg, you have the other numbers, calculate lambda. That will come out in meters.

Answer 9

2.66 X 10 ^-23 (0.001 kg/1 g) = 2.66X 10^-26

that is what I want is kg

Answer 10

right

Answer 11

so I don't need to go any father I just plug this back into the original problem and get my answer right

Answer 12

right. You have h, mass, velocity. That's all you need to calculate lambda.

Answer 13

6.63 X 10^-34/ (2.66X 10^-26 kg)(521 m/s) = 1.30 X 10^-5
is this correct

Answer 14

No, but I gave you a bum steer. I re-read the problem and the problem states that it is an oxygen molecule, not an oxygen atom. Therefore, the masss of the oxygen MOLECULE (instead of atom) is
32/6.02 x 10^23 = 5.32 x 10^-23 g or 5.32 x 10^-26 kg. Then
lambda = 6.63 x 10^-34/(5.32 x 10^-26 x 521) = ??
Check my work.