Answer:
8
Explanation:
The energy levels is given as
E(n) = n² * h² / ( 8 * m * L²), where
n = 1, 2, 3, 4,... etc
At ground state energy (n = 1), therefore is E(g) = h² / (8 * m * L²).
We can then say that
E(n) = n² * Eg
Therefore, to have E = 64 Eg, we must have n² = 64. And for n² to be equal to 64, we find the square root of n
n = √64
n = 8
Essentially, the needed quantum number is 8
