The angular momentum of an electron in the n-th orbit of a hydrogen atom is given by Bohr's quantization rule:
L=2πnh
Given that the angular momentum is π3h, we can equate the two expressions:
2πnh=π3h
Solving for n, we get:
n=6
The energy of an electron in the n-th orbit of a hydrogen atom is given by the formula:
En=−n213.6 eV
Substituting n=6 into the energy formula:
E6=−6213.6 eV
E6=−3613.6 eV
E6≈−0.377 eV≈−0.38 eV
Answer: −0.38