Energy levels A, B, C of a certain atom corresponds to increasing value of energy $E_A< E_B< E_C$. If $λ_1,λ_2,λ_3$ are the wavelengths of radiation corresponding to the transitions C → B, B → A and C → A respectively then:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ${λ_3}=\frac{λ_1λ_2}{λ_1+λ_2}$
The energy (E) is,
$E=\frac{hc}{λ}$
for the transition,
$C→B$, the energy different $E_{C→B}=E_C-E_B$
$B→A$, the energy different $E_{B→A}=E_B-E_A$
$C→A$, the energy different $E_{C→A}=E_C-E_A$
$λ_1=\frac{hc}{E_{C→B}},λ_2=\frac{hc}{E_{B→A}},λ_3=\frac{hc}{E_{C→A}}$
Now,
$E_{C→A}=E_{C→B}+E_{B→A}$
$⇒\frac{1}{λ_3}=\frac{1}{λ_1}+\frac{1}{λ_2}$
$⇒λ_3=\frac{λ_1λ_2}{λ_1+λ_2}$