Respuesta :
Answer:
Photons with different energy are
12.9 10⁻²⁸ J , 6.04 10⁻²⁸ J , 6.9 10⁻²⁸ J, 10.35 10⁻²⁸J, 2,588 10⁻²⁸J
Explanation:
The solution of the Schrödinger equation for an infinite square potential is relatively easy and results in the energy having the form
Eₙ = (h²/8mL²) n²
Where m is the mass of the electron, L the length of the box and n is a positive integer
Let's apply this equation the case that they give us
L = 0.70 nm = 0.70 10-9 m
E₀ = h² / 8mL²
E₀ = (6.63 10⁻³⁴)² / (8 9.1 10⁻³¹ 0.70 10⁻⁹)
E₀ = 0.8626 10⁻²⁸ J
Eₙ = E₀ n²
For the initial state n = 4
E₄ = Eo 4²
E₄ = 16 E₀
Let's write the possible transitions
Case first jump second jump
State: initial final initial final
1 4 1
2 4 3 3 1
3 4 2 2 1
Energy of emitted photons
Case 1
ΔE = E₄ -E₁
DE = 16 E₀ - Eo = 15 E₀
ΔE = 15 0.8626 10⁻²⁸ J
ΔE = 12.9 10⁻²⁸ J
Case 2
First photon
ΔE = E₄ -E₃
ΔE = 16E₀ - 9E₀ = 7 E₀
ΔE = 7 0.8626 10⁻²⁸ J
ΔE = 6.04 10⁻²⁸ J
Photon 2
ΔE = E₃-E₁
ΔE = 9E₀ - E₀ =8E₀
ΔE = 8 0.8626 10⁻²⁸ J
ΔE = 6.9 10⁻²⁸ J
Case 3
Photon 1
ΔE = E₄-E₂
ΔE = 16E₀-4E₀ = 12E₀
ΔE = 12 0.8626 10⁻²⁸ J
ΔE = 10.35 10⁻²⁸ J
Photon 2
ΔE = E₂-E₁
ΔE = 4E₀ -E₀ = 3E₀
ΔE = 3 0.8626 10⁻²⁸ J
ΔE = 2,588 10⁻²⁸ J
Photons with different energy are
- 12.9 10⁻²⁸ J
- 6.04 10⁻²⁸ J
- 6.9 10⁻²⁸ J
- 10.35 10⁻²⁸J
- 2,588 10⁻²⁸J
In total 5 photons of different energy are emitted
