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(D) The number of spectral lines emitted when an electron transitions from an excited state $n$ to the ground state is given by the formula $N = \frac

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$10$

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(D) The number of spectral lines emitted when an electron transitions from an excited state $n$ to the ground state is given by the formula $N = \frac{n(n-1)}{2}$.Given that the electron is in the $5^{th}$ orbit $(n = 5)$,the number of spectral lines is $N = \frac{5(5-1)}{2} = \frac{5 	imes 4}{2} = 10$.The possible transitions are:From $n=5$: $(5 	o 4), (5 	o 3), (5 	o 2), (5 	o 1)$From $n=4$: $(4 	o 3), (4 	o 2), (4 	o 1)$From $n=3$: $(3 	o 2), (3 	o 1)$From $n=2$: $(2 	o 1)$Total number of lines = $4 + 3 + 2 + 1 = 10$.

$A$ hydrogen atom in its ground state absorbs a photon and the electron transitions to the $5^{th}$ orbit. When the excited atom returns to its ground state,it emits photons of various energies. What is the maximum number of spectral lines that can be obtained in this process?

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