E = energy in nth state = 5.4 eV
E' = energy in (n + 1)th state = 9.6 eV
L = length of the box
m = mass of electron = 9.1 x 10⁻³¹ kg
h = plank's constant = 6.63 x 10⁻³⁴
Energy in nth state is given as
E = n²h²/(8 m L²) eq-1
Energy in (n+1) th state is given as
E' = (n + 1)²h²/(8 m L²) eq-2
dividing eq-1 by eq-2
E/E' = n²/(n + 1)²
inserting the values
5.4 /9.6 = n²/(n + 1)²
n = 3
using eq-1
E = n²h²/(8 m L²)
inserting the values
5.4 x 1.6 x 10⁻¹⁹ = (3)² (6.63 x 10⁻³⁴)²/(8 (9.1 x 10⁻³¹) L²)
L = 7.9 x 10⁻¹⁰ m
