(a) The quantum number for Bohr's orbit in a hydrogen atom is 443.
(b) The energy of the hydrogen atom is -1.11 x 10⁻²³ J.
Quantum number of the Bohr's orbit
According to Bohr's model, the radius of nth orbit is given as;
rₙ = r₀n²
where;
- r₀ is the radius of orbit at n = 1, r₀ = 0.51 x 10⁻¹⁰ m
n² = rₙ/r₀
n² = (1 x 10⁻⁵)/(0.51 x 10⁻¹⁰)
n² = 196,078.4
n = 442.8 ≈ 443
Energy of the hydrogen atom
[tex]E = -R_H[\frac{z^2}{n^2} ]\\\\E = -2.18 \times 10^{-18} [\frac{1^2}{443^2} ]\\\\E = -1.11 \times 10^{-23} \ J[/tex]
Learn more about Bohr's model here: https://brainly.com/question/18002213
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