Question

Energy levels A, B, C of a certain atom correspond to increasing values of energy, i.e., E_A< E_B< E_C. If l₁, l₂, l₃ are the wavelengths of radiation corresponding to the transitions C to B, B to A and C to A respectively, which of the following relations is correct?

• A. l₃ = l₁ + l₂
• B. l₃ = $\frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}$
• C. l₁ + l₂ + l₃ = 0
• D. $\lambda_{3}^{2} = \lambda_{1}^{2} + \lambda_{2}^{2}$

Answer 1

Answer: (B)

l₃ = $\frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}$

Answer 2

E = E₁ + E₂

$\frac{hc}{\lambda} = \frac{hc}{\lambda_{1}} + \frac{hc}{\lambda_{2}}$

$\frac{1}{\lambda} = \frac{1}{\lambda_{1}} + \frac{1}{\lambda_{2}}$

l = $\frac{\lambda_{1}\lambda_{2}}{\lambda_{1} + \lambda_{2}}$