Energy levels A, B and C of a certain action corresponding to increasing values of energy i.e. E_A < E_B < E_C . If λ_1 , λ_2 and λ_3 are wavelength of radiations corresponding to transitions C to B, B to A and C to A

Correct answer: B. λ_3=(λ_1 λ_2)/(λ_1+λ_2) E_A E_B F_C aligned E & =(h c)/(λ) E_ C A & =E_ C B +E_ B A (h c)/(λ_3)& =(h c)/(λ_1)+(h c)/(λ_2) (1)/(λ_3)& =(1)/(λ_1)+(1)/(λ_2) λ_3 & =(λ_1 λ_2)/(λ_1+λ_2) aligned

NEET 2005

Exam: NEET
Year: 2005
Subject: Physics
Chapter: Atomic Physics

NEET 2005 · Physics · Atomic Physics

Energy levels A, B and C of a certain action corresponding to...

Energy levels

\mathrm{A}, \mathrm{B}

and

\mathrm{C}

of a certain action corresponding to increasing values of energy i.e.

E_A < E_B < E_C

. If

\lambda_1

\lambda_2

and

\lambda_3

are wavelength of radiations corresponding to transitions

\mathrm{C}

\mathrm{B}, \mathrm{B}

\mathrm{A}

and

\mathrm{C}

\mathrm{A}

respectively, which of the following relations is correct? Energy levels A, B and C of a certain action corresponding to increasing values of energy i.e. E_A < E_B < E_C . If λ_1

Energy levels A, B and C of a certain action corresponding to increasing values of energy i.e. E_A < E_B < E_C . If λ_1

Options

A $\lambda_3=\lambda_1+\lambda_2$
B $\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}$
C $\lambda_1+\lambda_2+\lambda_3=0$
D $\lambda_3^2=\lambda_1^2+\lambda_2^2$

Correct answer

B. $\lambda_3=\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2}$

Step-by-step solution

E_A \lt E_B \lt F_C

\begin{aligned}E & =\frac{h c}{\lambda}\\ E_{C A} & =E_{C B}+E_{B A} \\ \frac{h c}{\lambda_3}& =\frac{h c}{\lambda_1}+\frac{h c}{\lambda_2}\\ \frac{1}{\lambda_3}& =\frac{1}{\lambda_1}+\frac{1}{\lambda_2}\\ \Rightarrow \quad \lambda_3 & =\frac{\lambda_1 \lambda_2}{\lambda_1+\lambda_2} \end{aligned}

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