The wavelength released in transition energy is 4.23 x 10¯⁶ 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
n1 = 5
n2 = 2
By substituting the following parameter, we get
ΔE = E2 - E1
ΔE = -(13.6) / n2² - (-(13.6) / n1²)
ΔE = -(13.6) / 2² - (-(13.6) / 5²)
ΔE = 0.544 - 0.85
ΔE = -0.306 eV
the energy is minus because it got released.
Calculate the wavelength released
ΔE = 0.306 eV
h.c / λ = 0.306 eV
4.136 x 10¯¹⁵ . 3 x 10⁸ / λ = 0.306
λ = 4.23 x 10¯⁶ m
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