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.  

freezing

deposition

condensation

explanation;

melting also called fusion is the process where solid becomes liquid, sublimation is the process where solid becomes gaseous without first changing to liquid, deposition involves change from gaseous to solid state, freezing involves change from liquid to solid, boiling or evaporation involves change of liquid to gaseous state, while condensation is the change from gaseous state to liquid state.

endothermic reactions involves absorption of heat from the surroundings or the environment while exothermic reactions involves loss of heat energy to the surroundings.

in this case, sublimation, evaporation and melting are endothermic reactions (gain energy from the environment) while, freezing, deposition and condensation are exothermic (loss of energy to the surroundings) reactions.

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day