Question

The ratio of the difference in energy of electron between the first and second Bohr's orbital to that between second and third Bohr orbital is
1. 1/3
2. 27/5
3. 9/4
4. 4/9

Answer 1

We know,

Energy of Bohr's orbit = -2π²z²e⁴m/n²h²

So,
For First Orbit = -2π²×z²e⁴m/h² (Since n=1)
For Second Orbit = -2π²×z²e⁴m/4h² (Since n=2)
For Third Orbit = -2π²×z²e⁴m/9h (Since n = 3)

Difference of energy from first to second orbit,
E2-E1 = -2π²×z²e⁴m/4h² - [-2π²×z²e⁴m/h²] = 3π²z²e⁴m/2h²

Difference of energy from second to third orbit,
E3-E2 = -2π²×z²e⁴m/9h² - [-2π²×z²e⁴m/4h²] = 5π²z²e⁴m/18h²

Thus ratio of energy of difference of energies of first to second and second to third is = E2-E1/E3-E2

= (3π²z²e⁴m/2h²)/(5π²z²e⁴m/18h²)

= 27/5

Hence, the answer is 27/5 which is option 2 of your question.

Answer 2

27/5

The ratio of the difference in energy between the first and the second Bohr orbit:

E2−E1=13.6×(1)2×(121−221)=13.6×43

The ratio of the difference in energy between the second and the third Bohr orbit:

E3−E2=13.6×(1)2×(221−321)=13.6×365

E3−E2/E2−E1=13.6×36513.6×43=27/5