In a certain of an electron transition in the hydrogen atoms from an initial state (1) to a final state (2), the difference in the orbit radius(r $_{1}$ - r $_{2}$ ) is 24 times the first Bohr radius. Identify the transition:

5 \to 1

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25 \to 1

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8 \to 3

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7 \to 5

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Solution

The correct option is A $5 \to 1$
The difference in the orbit radius is 24 times the first Bohr radius.
$r_{1} - r_{2} = 24 \times 0.529 A^{o}$
But the radius of nth orbit is
$r_{n} = 0.529 n^{2} A^{0}$
Hence, $0.529 n_{1} 62 - 0.529 n_{2}^{2} = 24 \times 0.529$
Hence,
$n_{1}^{2} - n_{2}^{2} = 24$
This is possible when $n_{1} = 5$ and $n_{2} = 1$
Hence, the transition is $5 \to 1$

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In a certain of an electron transition in the hydrogen atoms from an initial state (1) to a final state (2), the difference in the orbit radius(r1 - r2) is 24 times the first Bohr radius. Identify the transition:

The correct option is A 5→1The difference in the orbit radius is 24 times the first Bohr radius.r1−r2=24×0.529AoBut the radius of nth orbit is rn=0.529 n2A0Hence, 0.529 n162−0.529 n22=24×0.529Hence, n21−n22=24This is possible when n1=5 and n2=1Hence, the transition is 5→1

In a certain of an electron transition in the hydrogen atoms from an initial state (1) to a final state (2), the difference in the orbit radius(r $_{1}$ - r $_{2}$ ) is 24 times the first Bohr radius. Identify the transition: