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(D) For the transition from $2E$ to $E$:$\Delta E_1 = 2E - E = E = \frac{hc}{\lambda} \implies E = \frac{hc}{\lambda}$ (Equation $1$)For the transitio

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$3\lambda$

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(D) For the transition from $2E$ to $E$:$\Delta E_1 = 2E - E = E = \frac{hc}{\lambda} \implies E = \frac{hc}{\lambda}$ (Equation $1$)For the transition from $\frac{4E}{3}$ to $E$:$\Delta E_2 = \frac{4E}{3} - E = \frac{E}{3} = \frac{hc}{\lambda'}$ (Equation $2$)Substituting the value of $E$ from Equation $1$ into Equation $2$:$\frac{1}{3} \left( \frac{hc}{\lambda} \right) = \frac{hc}{\lambda'}$$\frac{1}{3\lambda} = \frac{1}{\lambda'} \implies \lambda' = 3\lambda$Therefore,the correct option is $(D)$.

The following diagram indicates the energy levels of a certain atom. When the system moves from the $2E$ level to the $E$ level,a photon of wavelength $\lambda$ is emitted. The wavelength of the photon produced during its transition from the $\frac{4E}{3}$ level to the $E$ level is

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