• Support PF! Buy your school textbooks, materials and every day products via PF Here!

Arithmetic Question Involving Quantum Physics

  • Thread starter Coop
  • Start date
40
0
1. Homework Statement

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. Homework 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
 

lightgrav

Homework Helper
1,248
30
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.
 

Want to reply to this thread?

"Arithmetic Question Involving Quantum Physics" You must log in or register to reply here.

Related Threads for: Arithmetic Question Involving Quantum Physics

  • Posted
Replies
4
Views
2K
Replies
1
Views
1K
  • Posted
Replies
3
Views
1K
  • Posted
Replies
3
Views
4K
Replies
1
Views
440
Replies
9
Views
5K

Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top