A heat engine with 0.300 mol of a monatomic ideal gas initially fills a 1000 cm3 cylinder at 500 K . The gas goes through the fo
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Answer:
n₁ = 3
Explanation:
The energy of the states in the hydrogen atom is explained by the Bohr model, the transitions heal when an electron passes from a state of higher energy to another of lower energy,
ΔE = - E₀ = - k²e² / 2m (1 /
²2 - 1 / n₀²)
The energy of this transition is given by the Planck equation
E = h f = h c / λ
h c / λ = -k²e² / 2m (1 / no ²- 1 / no²)
1 / λ = Ry (1/ ² - 1 / n₀²)
Let's apply these equations to our case
λ = 821 nm = 821 10⁻⁹ m
E = h c / λ
E = 6.63 10⁻³⁴ 3 10⁸/821 10⁻⁹
E = 2.423 10⁻¹⁹ J
Now we can use the Bohr equation
Let's reduce to eV
E = 2,423 10⁻¹⁹ J (1eV / 1.6 10⁻¹⁹) = 1,514 eV
- E₀ = -13.606 (1 /
² - 1 / n₀²) [eV]
Let's look for the energy of some levels
n (eV)
- E
(eV)
1 -13,606 E₂-E₁ = 10.20
2 -3.4015 E₃-E₂ = 1.89
3 -1.512 E₄- E₃ = 0.662
4 -0.850375
We see the lines of greatest energy for each possible series, the closest to our transition is n₁ = 3 in which a transition from infinity (n = inf) to this level has an energy of 1,512 eV that is very close to the given value