In an experiment an atom in an excited state sometimes decays directly to the ground state

PHYSICS · Multi-part · CBSE · Physics · Atoms · Atoms

Problem

In an experiment an atom in an excited state

E_3

sometimes decays directly to the ground state

E_0

, emitting a single photon of energy

4.86\,\text{eV}

. At other times it undergoes a two-step cascade

E_3\to E_1\to E_0

, emitting photons of energies

3.01\,\text{eV}

and

1.85\,\text{eV}

, respectively. Assume

E_0

is defined as

0\,\text{eV}

. (1) Calculate the energy of the intermediate state

E_1

relative to the ground state. (2) Demonstrate quantitatively that energy conservation holds for both the direct and cascade decays.