An electon in a box absorbs light. The longest wavelength in the absorbtion spectrum is 400 nm . How long is the box

6.03x 10^-10 m

Explanation:

Given that

E= hc/ wavelength

And also

E= h²n2/8mL²

Equating the two and if we say the transition was from energy level 1 to 2 then

E2 - E1 = h²2/(8mL²) x ( 2² - 1²) = 3h²2/(8mL²)

So

L² = 3 h lambda / (8mc)

= 3 x6.626 10^-34 kg m^2/s x 400 10^-9 m /( 8 x 9.11 x10^-31 kg x3.00 10^8 m/s)

= 36.4 x 10^-20 m^2

L = 6.03 x 10^-10 m

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