Respuesta :
The wavelength needed in transition energy is λ = 9.73 x 10¯⁸ m.
We need to know about transition energy to solve this problem. Electrons in a hydrogen atom can move to another level of energy. It is also called a transition. In this process, electrons will absorb or release their energy to move. The transition energy can be determined as
ΔE = E2 - E1
where ΔE is transition energy, E2 is the final state of energy and E1 is the initial state of energy.
The state energy of a hydrogen atom can be calculated by
E = -(13.6) / n² eV
E = h.c / λ
where n is the number of energy states, h is Planck constant (4.136 x 10¯¹⁵ eV/Hz), c is speed of light (3 x 10⁸ m/s) and λ is wavelength.
From the question above, we know that
n2 = 4
n1 = 1
By substituting the following parameter, we get
ΔE = E2 - E1
ΔE = -(13.6) / n2² - (-(13.6) / n1²)
ΔE = -(13.6) / 4² - (-(13.6) / 1²)
ΔE = 13.6 - 0.85
ΔE = 12.75 eV
Calculate the wavelength needed
ΔE = 12.75 eV
h.c / λ = 12.75
4.136 x 10¯¹⁵ . 3 x 10⁸ / λ = 12.75
λ = 9.73 x 10¯⁸ m
For more on transition energy at: https://brainly.com/question/19054395
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