1. Calculate the energy of an electron of the hydrogen atom when it is in the en

Question

1. Calculate the energy of an electron of the hydrogen atom when it is in the energy levels indicated: a) n = 3 b) n = 6 c) n = infinity 2. Using Bohr's Equation calculate the energy change experienced by an electron when it undergoes transitions between the following energy levels. a) n = 6 arrow 3 b) n = 6 arrow infinity 3. Using Bohr's Theory not Rydberg's equation) calculate the wavelength, in units of nanometers, of the electromagnetic radiation emitted for the electron transition n = 6 right arrow 3. (1 m = 10^9 nm). 4. In what region of the electromagnetic spectrum (UV? microwave? etc.) would the electromagnetic radiation occur for the transition n = 6 right arrow n = 3? (Hint: See the section on Electromagnetic Radiation in your chemistry text.

Explanation / Answer

1)

(a) n = 3

E = -13.6 / n^2   eV

E = -13.6 / 3^2 eV

E = - 1.51 eV

(b) n = 6

E = -13.6 / 6^2 eV

E = -0.38 eV

(c)    n = infinity

E = 0

2)

1/ = R[1/(n1^2) -1/(n2^2)]   ,   R = 1.09737×10^7 m-1

       = 1.09737×10^7   [1/3^2- 1/ 6^2]

       = 9.1 x 10^5 m-1

E = h C /    = (6.625 x 10^-34) x (3 x10^8) x 9.1 x 10^5

E = 1.81 x 10^-19 J

(b) similarly calculate this problem

(3) n = 6-------------> 3

1/ = 9.1 x 10^5 m-1

    = 1.099 x 10^-6 m

wave length = 1099 nm

4)

1099 nm is fall into the IR region

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