Question

What wavelengths appear in the system's emission spectrum? The allowed energies of a quantum system are 0 eV, 5.0 eV , and 7.0 eV .

Answer 1

Let us name the quantum states

State 1 = 0eV
State 2 = 5eV
State 3 = 7eV

The transitions in which the energy may be liberated (and emission spectra obtained) are :
State 2 ---> State 1
State 3 ---> State 2
State 3 ---> State 1

The energy liberated in the above transitions are 5eV, 2eV, 7eV respectively

Now use the Planck's law

Change in energy = h*c/d
h = Planck's constant =6.6 *10^-34 J s
c = 3*10^8 m/s
d is wavelength

Put the values of energy difference corresponding to each transition mentioned above to get corresponding wavelength .