Use the Bohr model to address this question. When a hydrogen atom makes a transition from the 4th energy level to the 2nd, counting the ground level as the first, what is the energy of the emitted photon? Express the answer in electron volts. Number eV What is the wavelength, in nanometers, of the emitted photon? Number nim What is the radius, in nanometers, of the hydrogen atom in its initial (4th) energy level? Number nm Solution energy in 4th level E4 = -13.6/4^2 eV E4 = -0.85 eV energy in 2nd level E2 = -13.6/2^2 eV E2 = -3.4 eV emitted energy E = E4 - E2 = -0.85 + 3.4 = 2.55 eV ===================== energy E = hc/lambda wavelength lambda = hc/E = (6.626*10^-34*3*10^8)/(2.55*1.6*10^-19) = 487.2 nm ========================== radius R = 0.053*n^2 Radius = R = 0.053*4^2 nm = 0.848 nm .

1. Use the Bohr model to address this question. When a hydrogen atom makes a transition from the
4th energy level to the 2nd, counting the ground level as the first, what is the energy of the
emitted photon? Express the answer in electron volts. Number eV What is the wavelength, in
nanometers, of the emitted photon? Number nim What is the radius, in nanometers, of the
hydrogen atom in its initial (4th) energy level? Number nm
Solution
energy in 4th level
E4 = -13.6/4^2 eV
E4 = -0.85 eV
energy in 2nd level
E2 = -13.6/2^2 eV
E2 = -3.4 eV
emitted energy E = E4 - E2 = -0.85 + 3.4 = 2.55 eV
=====================
energy E = hc/lambda
wavelength lambda = hc/E = (6.626*10^-34*3*10^8)/(2.55*1.6*10^-19) = 487.2 nm
==========================

2. radius R = 0.053*n^2
Radius = R = 0.053*4^2 nm = 0.848 nm