Final answer:
The ratio of the difference between 2nd and 3rd Bohr orbit energy to that between 3rd and 4th orbit energy, according to the Bohr model, is 3/2 or 1.5.
Step-by-step explanation:
To find the ratio of the difference between the 2nd and 3rd Bohr orbit energy to that between the 3rd and 4th orbit energy, we use the formula ΔE = E_{final} - E_{initial}, where ΔE is the change in energy, E_{final} is the energy of the final orbit, and E_{initial} is the energy of the initial orbit. From Bohr's model, we know the energy of an electron in a given orbit is proportional to -1/n2, where n is the principal quantum number of the orbit. Therefore, the energies for the orbits n=2, 3, and 4 are respectively proportional to -1/22, -1/32, and -1/42.
The energy difference between the 2nd and 3rd orbits is ΔE_{2-3} = (1/32) - (1/22) = (1/9) - (1/4) = (1/9) - (4/36) = (1-4)/36 = -3/36 = -1/12.
The energy difference between the 3rd and 4th orbits is ΔE_{3-4} = (1/42) - (1/32) = (1/16) - (1/9) = (1/16) - (9/144) = (1-9)/144 = -8/144 = -1/18.
Finally, the ratio ΔE_{2-3}/ΔE_{3-4} = (-1/12)/(-1/18) = 18/12 = 3/2 or 1.5.