(i) The energy associated with the first orbit in the hydrogen atom is –2.18 × 10 –18 J atom –1 . What is the energy associated with the fifth orbit? (ii) Calculate the radius of Bohr’s fifth orbit for hydrogen atom.
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1) energy of an atom in an orbit = -13.6eV÷n²
n is the principal quantum number.
in the first orbit , the energy is (-13.6×1.6×10^-19)÷1²
so , the energy is -2.18×10^-18 J.
so in the fifth orbit, energy = (-13.6×1.6×10^-19)÷5²
energy = -8.704×10^-20 J
2) Bohr radius = 0.53×10^-10× n²
in fifth orbit ,
Bohr radius = (0.53×10^-10)×5²
Bohr radius = 1.325×10^-9 .
n is the principal quantum number.
in the first orbit , the energy is (-13.6×1.6×10^-19)÷1²
so , the energy is -2.18×10^-18 J.
so in the fifth orbit, energy = (-13.6×1.6×10^-19)÷5²
energy = -8.704×10^-20 J
2) Bohr radius = 0.53×10^-10× n²
in fifth orbit ,
Bohr radius = (0.53×10^-10)×5²
Bohr radius = 1.325×10^-9 .
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