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(D) The energy of a photon emitted during a transition is given by $\Delta E = E_i - E_f = \frac{hc}{\lambda}$.Since $\lambda = \frac{hc}{\Delta E}$,t

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$n = 5$ to $n = 2$

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(D) The energy of a photon emitted during a transition is given by $\Delta E = E_i - E_f = \frac{hc}{\lambda}$.Since $\lambda = \frac{hc}{\Delta E}$,the wavelength $\lambda$ is inversely proportional to the energy difference $\Delta E$ of the transition.Emission occurs when an electron moves from a higher energy level to a lower energy level.Comparing the given transitions:$(A)$ $n = 2$ to $n = 1$: Large energy difference.$(B)$ $n = 1$ to $n = 2$: Absorption,not emission.$(C)$ $n = 2$ to $n = 5$: Absorption,not emission.$(D)$ $n = 5$ to $n = 2$: Smaller energy difference compared to $n = 2$ to $n = 1$.Since $\Delta E$ for $n = 5 	o 2$ is smaller than $\Delta E$ for $n = 2 	o 1$,the wavelength $\lambda$ for the $n = 5 	o 2$ transition will be larger.Therefore,the correct option is $(D)$.

Which of the following transitions will have the highest emission wavelength?

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