Our understanding of the h atom will us learn about atoms with more electrons. the n =1 electron energy level of a h atom has an energy of 2.18  10–18 j. (a) what is the energy of the n = 5 level? (b) calculate the wavelength and frequency of a photon emitted when an electron jumps down from n = 5 to n = 1 in a h atom.

a) What is the energy of the n = 5 level?

(b) Calculate the wavelength and frequency of a photon emitted when an electron jumps down from n = 5 to n = 1 in a H atom.

,

Explanation:

The permitted energy for the atom of hydrogen according with the Bohr's model is defined as:

 (1)

Or it can be expressed in Joules, since

Where the value represents the energy of the ground state¹ and n is the principal quantum number.

a) What is the energy of the n = 5 level?

For the case of :

So the energy of the level is .   

(b) Calculate the wavelength and frequency of a photon emitted when an electron jumps down from n = 5 to n = 1 in a H atom.

The wavelength can be determined by means of the Rydberg formula:

 (2)

Where R is the Rydberg constant, with a value of

For this particular case and :

Where

.  

The frequency can be found by means of:

  (3)

Equation (3) can be rewritten in terms of :

Where

Key terms:

¹Ground state: State of minimum energy.  

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