A hydrogen atom absorbs energy and rises to n = 3 state from its ground state n = 1. If the potential energy of the atom at its ground state is -13.6eV, find the wave length emitted by it when it returns to its ground state: Planck's constant= 6.6 10³⁴ J s

Step-by-step solution

Total energy of hydrogen atom in ground state, E₁ = -13.6 eV Energy in n=3 state, E₃ = -13.6 3^2 = -1.51 eV Energy of emitted photon, E = E₃ - E₁ = -1.51 - (-13.6) = 12.09 eV Wavelength of emitted photon, = hc E = 6.6 10⁻³⁴ 3 10^8 12.09 1.6 10⁻¹⁹ = 19.8 10⁻²⁶ 19.34 10⁻¹⁹ 1.023 10⁻⁷ m 1023 Å 1020 Å Answer: 1020Å