Question

What photon wavelength is emitted when an electron in a hydrogen atom drops from an orbit with a radius of 3.3856x10m to the ground state?

Answer 1

in - J.S e In a hydrogen atom, radius of noth orbit is given by n²h² 47² kme22 whene, h is planck h is planck constant = 6.626x10 34 m is mass of electron = 9.1 x 1731 kg is change of electron of electron = 1-6x 1019 K is Coulomb constant = 9x109 N-m? c? z = atomic number of atom = 1 47² 4m ke² rn h2 47?(1)(9-18 1719(9x 10°) C1-6x10193263-3856x179) (6.626 X163432 n قدر/ 2. ni 1.2= 7.99 Ñ 8 2=8 The electron drops from an orbit 2=8 to the ground state (n=1) If the wavelength of thoton emitted is a, he Ephoton a E Enal he N=8 a وفا No En=1 13.6 - 13.6 eV n² 13.6 (8)2 -0.2125 eV En=8 -0.2125 eV - L-13.6 ev) he he = 13-3875 2 he 1240 ev-nm .: 13.3875 eV 13.38 75 ev = 92.62 nm :. The photon wavelength is a= 92.62 mm

Wavelength of photon emitted is related to the energy of photon E by the relation E = (h•c)/wavelength.