Answer:
91.6 nm
Explanation:
The energy of the hydrogen atom can be calculated by the emission of a photon. When an electron is excited it goes from to the next energetic level, and when it returns to its ground state, it emits a photon. Hydrogen has only one electron, which is at the level n = 1. So, the equation is given:
E = (-21.7x10⁻¹⁹J)/1²
E = -21.7x10⁻¹⁹J
The energy of the photon is the energy absorbed, and because of that is positive (the opposite of the energy released by the electron). This energy can be calculated by:
E = h*c/λ
Where h is the Planck's constant (6.626x10⁻³⁴ J.s), c is the speed of the light (3.00x10⁸ m/s), and λ is the wavelength of the photon.
21.7x10⁻¹⁹ = 6.626x10⁻³⁴ * 3.00x10⁸/λ
λ = 9.16x10⁻⁸ m
λ = 91.6 nm
