(B) The radius of the $n^{\text{th}}$ Bohr orbit is given by the formula $r_{n} = a_{0} \times \frac{n^{2}}{Z}$,where $a_{0}$ is the Bohr radius,$n$ i

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(B) The radius of the $n^{\text{th}}$ Bohr orbit is given by the formula $r_{n} = a_{0} \times \frac{n^{2}}{Z}$,where $a_{0}$ is the Bohr radius,$n$ is the principal quantum number,and $Z$ is the atomic number.For a hydrogen atom,$Z = 1$.Thus,$r_{n} \propto n^{2}$.For the $3^{\text{rd}}$ orbit,$r_{3} \propto 3^{2} = 9$.For the $4^{\text{th}}$ orbit,$r_{4} \propto 4^{2} = 16$.Taking the ratio,$\frac{r_{4}}{r_{3}} = \frac{16}{9}$.Therefore,$r_{4} = \frac{16}{9} r_{3}$.

Class 11 Chemistry Structure of Atom Atomic models and Planck's quantum theory

Medium

If the radius of the $3^{\text{rd}}$ Bohr's orbit of hydrogen atom is $r_{3}$ and the radius of $4^{\text{th}}$ Bohr's orbit is $r_{4}$,then which of the following relations is correct?

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A
$r_{4} = \frac{9}{16} r_{3}$
B
$r_{4} = \frac{16}{9} r_{3}$
C
$r_{4} = \frac{3}{4} r_{3}$
D
$r_{4} = \frac{4}{3} r_{3}$

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If the radius of the $3^{\text{rd}}$ Bohr's orbit of hydrogen atom is $r_{3}$ and the radius of $4^{\text{th}}$ Bohr's orbit is $r_{4}$,then which of the following relations is correct?

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What is the wavenumber of the photon emitted during transition from the orbit $n=5$ to that of $n=2$ in hydrogen atom (in $cm^{-1}$)?
$\left[R_{H}=109677 \ cm^{-1}\right]$