(B) The radius of the $n^{th}$ orbit of a hydrogen-like species is given by $r_n = a_0 \times \frac{n^2}{Z}$, where $a_0$ is the Bohr radius $(52.9 \t

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(B) The radius of the $n^{th}$ orbit of a hydrogen-like species is given by $r_n = a_0 \times \frac{n^2}{Z}$, where $a_0$ is the Bohr radius $(52.9 \text{ pm})$.For $H$ atom $(Z=1)$: $x = r_3 - r_2 = a_0 \times (3^2 - 2^2) / 1 = a_0 \times (9 - 4) = 5a_0$.For $Li^{2+}$ ion $(Z=3)$: $y = r_4 - r_3 = a_0 \times (4^2 - 3^2) / 3 = a_0 \times (16 - 9) / 3 = \frac{7}{3}a_0$.The ratio $y:x = (\frac{7}{3}a_0) : (5a_0) = \frac{7}{3} : 5 = 7 : 15$.

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

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The difference between the radii of $3^{rd}$ and $2^{nd}$ orbit of $H$ atom is $x \text{ pm}$. The difference between the radii of $4^{th}$ and $3^{rd}$ orbit of $Li^{2+}$ ion is $y \text{ pm}$. The ratio $y:x$ is equal to:

AP EAMCET 2025 All AP EAMCET

A
$15:7$
B
$7:15$
C
$3:1$
D
$1:3$

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Structure of Atom

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Atomic models and Planck's quantum theory

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The difference between the radii of $3^{rd}$ and $2^{nd}$ orbit of $H$ atom is $x \text{ pm}$. The difference between the radii of $4^{th}$ and $3^{rd}$ orbit of $Li^{2+}$ ion is $y \text{ pm}$. The ratio $y:x$ is equal to:

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What is the name by which Thomson's atomic model is known?

The electron in a hydrogen atom is in the first Bohr orbit $(n=1)$. The ratio of transition energies,$E(n=1 \rightarrow n=3)$ to $E(n=1 \rightarrow n=2)$,is

What is the maximum number of emission lines when the excited electron of an $H$ atom in $n=6$ drops to the ground state?

The energy of an electron in the first Bohr orbit of $H$ atom is $-13.6 \ eV$. The energy value of an electron in the first excited state of $Li^{2+}$ is ............... $eV$.

The ratio of the radii of two Bohr orbits of a hydrogen atom is $4:1$. What are their designations?

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