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The ratio of the difference between 2nd and 3rd bohr's orbit energy to that between 3rd and 4th orbit energy is???

The ratio of the difference between 2nd and 3rd bohr's orbit energy to that between 3rd and 4th orbit energy is???

Grade:9

1 Answers

Arun
25750 Points
5 years ago
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
 

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