The energy E of the electron in a hydrogen atom can be calculated from the Bohr

Question

The energy E of the electron in a hydrogen atom can be calculated from the Bohr formula: equation R, stands for the Rydberg energy, and n stands for the principal quantum number of the orbital that holds the electron. (You can find the value of the Rydberg energy using the Data button on the ALEKS toolbar) Calculate the wavelength of the line in the absorption li with n-10 Round your answer to 3 significant digits ne spectrum of hydrogen caused by the transition of the electron from an orbital with n -3 to an orbital

Explanation / Answer

Ry value is 1.097 x 10^7 m -1 ,

for n = 3 we get E =- ( Ry) / 3^2 = -Ry / 9

when n = 10 we get E = -( Ry) / ( 10^2) = - ( Ry /100)

Energy difference between them E(n=10) - E( n = 3) = - Ry ( 1/100 - 1/9)   = Ry ( 1/9 - 1/100)

             = 1.097 x 10^7 m-1 ( 0.1011)

               = 1.1092 x 10^6 m-1

wavelength = 1 / wavenumber = ( 1/ 1.1092 x 10^6 m-1) = 9.16 x 10^-7 m = 916 x 10^-9 m = 916 nm

( since 1nm= 10^-9 m)

Thus the wavelength correspods to transtion is 916 nm

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