Quantum mechanics shows that an electron having m=9.109390 x 10^-31 kg and confi

Question

Quantum mechanics shows that an electron having m=9.109390 x 10^-31 kg and confined to a box of length L=1.6x10^-10m, can have the following quantized energies: En= n^2h^2/8mL^2 where h = plancks?s constant = 6.6256 X 10^-34 J s and n is a quantum number n = 1,2 , . . . . If the electron makes a transition from the n=3 state to the n=1 state,what is the wavelength of the emitted photon? Use the following crude table to predict in what region of the electromagnetic spectrum this radiations will be found.

Explanation / Answer

wavelength is given by the formula , (1/wavelenght) = R ( 1/n1^2 - 1/n2^2 )

here n1 = 1 , n2 =3 ( n2 is the state from which it transits , n1 is the state to which it transists ) ,

R = rydberg's constant = 10^7 m-1

1/wavelngth = ( 10^7) ( 1- 1/9)

wavelength = 1.125*10-7 m = 112.5nm

so this radiation comes under UV region

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