Respuesta :
Answer:
Initial state Final state
3 ⇒ 2
3 ⇒ 1
2 ⇒ 1
Explanation:
For this exercise we must use Bohr's atomic model
E = - 13.606 / n²
where is the value of 13.606 eV is the energy of the ground state and n is the integer.
The energy acquired by the electron in units of electron volt (eV)
E = e V
E = 12.5 eV
all this energy is used to transfer an electron from the ground state to an excited state
ΔE = 13.6060 (1 / n₀² - 1 / n²)
the ground state has n₀ = 1
ΔE = 13.606 (1 - 1/n²)
1 /n² = 1 - ΔE/13,606
1 / n² = 1 - 12.5 / 13.606
1 / n² = 0.08129
n = √(1 / 0.08129)
n = 3.5
since n is an integer, maximun is
n = 3
because it cannot give more energy than the electron has
From this level there can be transition to reach the base state.
Initial state Final state
3 ⇒ 2
3 ⇒ 1
2 ⇒ 1
The possible quantum-jump transitions by which the excited atom emits a photon are :
Initial state Final state
3 ---> 2
3 ----> 1
2 ----> 1
Given data :
Potential difference through which an electron accelerates = 12.5 V
Energy acquired by the the electrons = 12.5 eV ( e * 12.5 )
The Model we will use to determine the possible quantum jump transition is Bohr's atomic model
E = - 13.606 / n²
where ; n = integer
energy at ground state = 13.606 eV
The energy acquired by the electrons ( 12.5 eV ) is used to move the electron from its ground state to an excited state.
Therefore
ΔE = 13.606 * (1 / n₀² - 1 / n²) ---- ( 1 )
where n₀ = 1
Back to equation ( 1 )
ΔE = 13.606 (1 - 1/n²) -- ( 2 )
Resolving equation ( 2 )
1 / n² = 0.08129
n = 3.5 . Therefore the maximum integer = 3
Hence The collision between the electron and the hydrogen atom will undergo three ( 3 ) transition to reach the base state.
In Conclusion The possible quantum-jump transitions by which the excited atom emits a photon are :
Initial state Final state
3 ---> 2
3 ----> 1
2 ----> 1
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