Calculate the wavelength of the light emitted when an electron in a one-dimensional box of length 5.2nm makes a transition from the n = 7 state to the n = 6 state. Express your answer with the appropriate units. I calculated in this way: E = n^2*h^2/8*m*a^2 E= (7^2-6^2)*(6.626*10^-34)^2/8*(9.1*10^-31)*(5.2*10^-9)^2 E= 2.9*10^-20 J E = hc/λ λ = 6.85*10^-6 m But the answer is wrong. What is wrong with my calculation?
How do you know the answer is wrong? It can help if you do the algebra first, then use more convenient units:$$\lambda=\frac{8(m_e c^2) L^2}{hc}\frac{1}{n_f^2-n_i^2}$$ ##hc=1.240\text{eV$\mu$m}## ##m_ec^2=511\text{eV}## ##L=0.0052\text{$\mu$m}## ... give it a go. (Don't forget to check my algebra to get that equation.)
It is the same calculation as mine. I did the exercise on MasteringChemistry. It only said my answer is wrong.
But I got a different order of magnitude from you. Repeat the calculation ... you have misplaced a decimal point someplace.