Which among the following electron transition | vedclass

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(B) The radius of an orbit in a hydrogen-like atom is given by $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.
The change in radius is $\Delta r =

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$5 \rightarrow 4$

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(B) The radius of an orbit in a hydrogen-like atom is given by $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.
The change in radius is $\Delta r = r_2 - r_1 = \frac{0.529}{Z} 	imes (n_2^2 - n_1^2)$.
For a $H$-atom,$Z = 1$,so $\Delta r = 0.529 	imes (n_2^2 - n_1^2)$.
Calculating $\Delta r$ for each option:
$A) \ 4 ightarrow 1: \Delta r \propto (4^2 - 1^2) = 16 - 1 = 15$
$B) \ 5 ightarrow 4: \Delta r \propto (5^2 - 4^2) = 25 - 16 = 9$
$C) \ 6 ightarrow 5: \Delta r \propto (6^2 - 5^2) = 36 - 25 = 11$
$D) \ 4 ightarrow 2: \Delta r \propto (4^2 - 2^2) = 16 - 4 = 12$
The minimum value is $9$,which corresponds to the transition $5 ightarrow 4$.

Which among the following electron transitions $(n_2 \rightarrow n_1)$ in a $H$-atom results in the minimum change in its orbit radius $(r_2 - r_1)$?

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