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: E = - R_y/n^2 In this equation R_y 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 emission line spectrum of hydrogen caused by the transition of the electron from an orbital with n = 9 to an orbital with n = 5. Round your answer to 3 significant digits.

Explanation / Answer

From Rydburg's Equation , 1/ = R[(1/ni2) – (1/nf2)]
   Where R = Rydburg's constant = 10.96 x106 m-1
               = wavelength = ?
               ni = 5
               nf = 9
Plug the values we get

1/ = 10.96 x106 x[(1/52) – (1/92)]

       = 303.1x103

= 3.29x10-6 m

Therefore the wavelength of emitted light is 3.29x10-6 m

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