Answer
a. -5.08 eV. b. -5.63 eV
Work Step by Step
Apply conservation of energy to the system. When an atom absorbs a photon, the energy of the atom goes up. When an atom emits a photon, the energy of the atom goes down.
a. Find the photon energy.
$$E=hf=h\frac{c}{\lambda}$$
$$E=\frac{1.24\times10^{-6}eV\cdot m}{860\times10^{-9}m }= 1.44eV$$
The internal energy of the atom increases by 1.44 eV, from -6.62 eV to -5.08 eV.
b. Find the photon energy.
$$E=hf=h\frac{c}{\lambda}$$
$$E=\frac{1.24\times10^{-6}eV\cdot m}{420\times10^{-9}m }= 2.95eV$$
The internal energy of the atom decreases by 2.95 eV, from -2.68 eV to -5.63 eV.
