1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculating the velocity of a molecule

  1. May 31, 2017 #1
    Hi, I'm stuck on a problem. I have this function that represents the velocity:

    T is the temperature and equals 293.15K
    m = 4.65 .10-26 kg
    k = 1.38 .10-23 J/K

    The problem wants us to find the derivative of the function. I found:
    df/dv= (2v) e(-mv2)/(2kT)+v2e(-mv2)/(2kT)(-2mv/2kT)
    = ve(-mv2)/(2kT) (2- (mv2/kT))

    I know the derivative I found is right, but now, I have to find the velocity for df/dv=0

    We know v>0 and ex>0
    So, df/dv=0 => (mv2)/kT = 2
    => v= √(2kT/m)

    That's where I'm stuck. The book tells me the answer is 1500km/h.
    I don't understand this solution. I calculated many many times and didn't found the right solution. Can someone please help me? :cry:
  2. jcsd
  3. May 31, 2017 #2


    User Avatar
    Science Advisor

    What answer did you get? Did you get 417? What are the units of that?
    If you got a different answer, can you show us exactly how you got it? Your formula looks right.
  4. May 31, 2017 #3
    Yes, I got 417!
    I just plugged in all the values in the last equation that I wrote, v= √(2kT/m).
    Since k is in J/K, T in K and m in kg, the unit of v is J/kg.
    J also equals kg m2 s-2 so I assume the unit of v can also be m2s-2?
  5. May 31, 2017 #4
    Oh, I got it! My answer is then in m.s-1 and I just need to multiply by 3.6.
    417*3.6=1501 km.h-1

    Thank you for the help :)
  6. May 31, 2017 #5


    User Avatar
    Science Advisor

    Can't emphasise enough the importance of thinking UNITS, UNITS, UNITS; ALWAYS, ALWAYS, ALWAYS! It will save you a lot of trouble and avoid a lot of mistakes, both with homework questions like this and real problems in doing science.
    For example, if you are asked for a velocity, the answer CANNOT be (e.g.) 417. It must be 417 SOMETHING - m/s, km/h, furlongs per fortnight or whatever. If you did that you would immediately see that your answer was not necessarily wrong, but another step was needed.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Calculating the velocity of a molecule