In a hydrogen atom,which of the following tra | vedclass

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(D) The wavelength $\lambda$ of a photon emitted during a transition is given by the Rydberg formula: $\frac{1}{\lambda} = R \left( \frac{1}{n_f^2} -

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$n = 2$ to $n = 1$

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(D) The wavelength $\lambda$ of a photon emitted during a transition is given by the Rydberg formula: $\frac{1}{\lambda} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} ight)$.This implies that $\lambda$ is inversely proportional to the energy difference $\Delta E$ of the transition,where $\Delta E = 13.6 \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} ight) 	ext{ eV}$.To have the minimum wavelength,the energy difference $\Delta E$ must be maximum.Comparing the transitions:$(A)$ $\Delta E \propto (1/16 - 1/25) = 0.0225$$(B)$ $\Delta E \propto (1/9 - 1/16) = 0.0486$$(C)$ $\Delta E \propto (1/4 - 1/9) = 0.1389$$(D)$ $\Delta E \propto (1/1 - 1/4) = 0.7500$The transition from $n = 2$ to $n = 1$ results in the largest energy change,and therefore,the minimum wavelength.

In a hydrogen atom,which of the following transitions will have the minimum wavelength?

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