(A) In Bohr's atomic model,the radius of the $n^{th}$ orbit is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$,which implies $r \propto n^2$.

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$E \propto -1/n^2, r \propto n^2$

(A) In Bohr's atomic model,the radius of the $n^{th}$ orbit is given by $r_n = \frac{n^2 h^2 \epsilon_0}{\pi m Z e^2}$,which implies $r \propto n^2$. The total energy of an electron in the $n^{th}$ orbit is $E_n = -\frac{m Z^2 e^4}{8 \epsilon_0^2 h^2 n^2}$,which implies $E \propto -1/n^2$. Considering the magnitude of energy,the relationship is $r \propto n^2$ and $E \propto 1/n^2$.

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

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In Bohr's atomic model,the radius $(r)$ and energy $(E)$ of an orbit $(n)$ are related as:

A
$E \propto -1/n^2, r \propto n^2$
B
$r \propto 1/n^2, E \propto n^2$
C
$r \propto 1/n, E \propto n$
D
$r \propto n^2, E \propto 1/n^2$

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Structure of Atom

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Atomic models and Planck's quantum theory

In a $He^{+}$ ion,an electronic transition occurs from orbit $n_2$ to $n_1$ such that:
$2n_2 + 3n_1 = 18$
$2n_2 - 3n_1 = 6$
What is the total number of photons emitted when the electron transitions to the $n_1$ orbit?

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Give reasons for the failure of the Bohr Model.

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If the radius of the hydrogen atom is $53 \, pm$, the radius of the $He^{+}$ ion is closest to $...... \, pm$.

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In Bohr's model of the atom,when an electron jumps from $n=1$ to $n=3$,how much energy will be absorbed?

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The wavelength of radiation emitted when an electron falls from the $4^{th}$ Bohr orbit to the $2^{nd}$ in an $H$ atom is .............. $nm$.

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In Bohr's atomic model,the radius $(r)$ and energy $(E)$ of an orbit $(n)$ are related as:

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In a $He^{+}$ ion,an electronic transition occurs from orbit $n_2$ to $n_1$ such that: $2n_2 + 3n_1 = 18$ $2n_2 - 3n_1 = 6$ What is the total number of photons emitted when the electron transitions to the $n_1$ orbit?

Give reasons for the failure of the Bohr Model.

If the radius of the hydrogen atom is $53 \, pm$, the radius of the $He^{+}$ ion is closest to $...... \, pm$.

In Bohr's model of the atom,when an electron jumps from $n=1$ to $n=3$,how much energy will be absorbed?

The wavelength of radiation emitted when an electron falls from the $4^{th}$ Bohr orbit to the $2^{nd}$ in an $H$ atom is .............. $nm$.

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In a $He^{+}$ ion,an electronic transition occurs from orbit $n_2$ to $n_1$ such that:
$2n_2 + 3n_1 = 18$
$2n_2 - 3n_1 = 6$
What is the total number of photons emitted when the electron transitions to the $n_1$ orbit?