# Dimensional analysis - quantum and classical lengthscale ratio

1. Apr 21, 2012

### kapitan90

1. The problem statement, all variables and given/known data
I was supposed to use dimensional analysis to approximate the length scale (in classical and quantum mechanics). The results I got(same as those in the answer sheet): classicaly$$l_c≈\frac{e^2}{4πm_ec^2ε_0}≈2.8*10^-15m$$ In quantum mechanics$$l_q≈\frac{h}{m_ec}≈2.4*10^-12m$$

2. Relevant equations
The next question is: how would your analysis in case of $$l_q$$have to change if $$l_q≈l_c?$$

3. The attempt at a solution
I have the answer to question b), but I don't think I understand it. The answer they give is:
'If$$l_q≈l_c$$ it would not be possible to estimate l_q without considering electromagnetic effects and write $$l_q=f(\frac{l_c}{l_q})$$ In fact ratio l_c/l_q is is small (apart from a factor of 2π it is just the fine structure constant).'