The energy levels of a certain atom for first, second and third levels are E, 4 (E/3) and 2 E respectively. A photon of wavelength λ is emitted for a transition 3 arrow 1. What will be the wavelength of emission for transition 2 arrow 1 ?

Question

The energy levels of a certain atom for first, second and third levels are E, 4 (E/3) and 2 E respectively. A photon of wavelength λ is emitted for a transition 3 arrow 1. What will be the wavelength of emission for transition 2 arrow 1 ? (A) (λ/3) (B) 3 λ (C) (3 λ/4) (D) (4 λ/3)

Tardigrade Admin · Accepted Answer

Δ E=2 E-E=(h c/λ1) ∴ E=(h c/λ1) Similarly (4 E/3)-E=(h c/λ2) ∴ (E/3)=(h c/λ2) ∴ λ2=3 λ1

Q. The energy levels of a certain atom for first, second and third levels are $E, 4 \frac{E}{3}$ and $2 E$ respectively. A photon of wavelength $λ$ is emitted for a transition $3 \to 1$ . What will be the wavelength of emission for transition $2 \to 1 ?$

$\frac{λ}{3}$

$3 λ$

$\frac{3 λ}{4}$

$\frac{4 λ}{3}$

$Δ E = 2 E - E = \frac{h c}{λ _{1}}$
$∴ E = \frac{h c}{λ _{1}}$
Similarly $\frac{4 E}{3} - E = \frac{h c}{λ _{2}}$
$∴ \frac{E}{3} = \frac{h c}{λ _{2}}$
$∴ λ_{2} = 3 λ_{1}$

Q. The energy levels of a certain atom for first, second and third levels are E,43E​ and 2E respectively. A photon of wavelength λ is emitted for a transition 3→1. What will be the wavelength of emission for transition 2→1?

3λ​

3λ

43λ​

34λ​