1. Not finding help here? Sign up for a free 30min 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!

Arithmetic Question Involving Quantum Physics

  1. Apr 23, 2014 #1
    1. The problem statement, all variables and given/known data

    Two adjacent allowed energies of an electron in a one-dimensional box are 2.0 eV and 4.5 eV. What is the length of the box?

    2. Relevant equations

    [tex]E_n=\frac{h^2n^2}{8mL^2}[/tex]

    3. The attempt at a solution

    My question is, since E_n and n^2 are both on separate sides of the equation in the numerator, why can't I put Delta in front of each of these variables and solve for L?

    [tex]\Delta E_n=\frac{h^2\Delta n^2}{8mL^2}[/tex] and since the energy levels are adjacent, [tex]\Delta n^2=1[/tex]

    I tried doing this, but it gave me the incorrect answer. I know how I am supposed to do the problem now, I am just wondering why my original technique does not work.

    Thanks,
    Cooper
     
  2. jcsd
  3. Apr 23, 2014 #2

    lightgrav

    User Avatar
    Homework Helper

    Delta is shorthand for small change; essentially a derivative.
    when you change n^2 to (n+1)^2 , it is not really a small change,
    and clearly the change in the second depends on n.
    (that is, 1^2 is 1, but 2^2 = 4 ... a difference of 3
    5^2 = 25 , but 6^2 = 36 ... a difference of 11 , which is 3½ times as much.
     
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: Arithmetic Question Involving Quantum Physics
Loading...