What is the wavelength of the light？

[atsum]

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?

 

[Simon Bridge]

How do you know the answer is wrong?

It can help if you do the algebra first, then use more convenient units:$$\lambda=\frac{8(m_e c^2) L^2}{hc}\frac{1}{n_f^2-n_i^2}$$

$hc=1.240\text{eV\mum}$
$m_ec^2=511\text{eV}$
$L=0.0052\text{\mum}$
... give it a go.
(Don't forget to check my algebra to get that equation.)

 

[atsum]

How do you know the answer is wrong?

It can help if you do the algebra first, then use more convenient units:$$\lambda=\frac{8(m_e c^2) L^2}{hc}\frac{1}{n_f^2-n_i^2}$$

$hc=1.240\text{eV\mum}$
$m_ec^2=511\text{eV}$
$L=0.0052\text{\mum}$
... 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.

 

[Simon Bridge]

But I got a different order of magnitude from you.
Repeat the calculation ... you have misplaced a decimal point someplace.