(D) According to Bohr's theory,the radius of the $n^{th}$ orbit is given by the formula:$r_n = 0.529 \times \frac{n^2}{Z} \, \mathring{A}$For the seco

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(D) According to Bohr's theory,the radius of the $n^{th}$ orbit is given by the formula:$r_n = 0.529 \times \frac{n^2}{Z} \, \mathring{A}$For the second Bohr orbit of the hydrogen atom,$n = 2$ and $Z = 1$.Substituting these values:$r_2 = 0.529 \times \frac{2^2}{1} \, \mathring{A}$$r_2 = 0.529 \times 4 \, \mathring{A} = 2.116 \, \mathring{A}$Rounding to two decimal places,we get $2.12 \, \mathring{A}$.

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

Medium

The radius of the second Bohr orbit for hydrogen atom is .......... $\mathring{A}$.
(Planck's constant $h = 6.626 \times 10^{-34} \, Js$; mass of electron $= 9.1091 \times 10^{-31} \, kg$; charge of electron $e = 1.60210 \times 10^{-19} \, C$; permittivity of vacuum $\epsilon_0 = 8.854185 \times 10^{-12} \, C^2 N^{-1} m^{-2}$)

JEE MAIN 2017 All JEE MAIN

A
$1.65$
B
$4.76$
C
$0.529$
D
$2.12$

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Class 11

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Structure of Atom

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Atomic models and Planck's quantum theory

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For hydrogen-like species,which of the following graphs provides the most appropriate representation of $E$ vs $Z$ plot for a constant $n$?
[$E$: Energy of the stationary state,$Z$: atomic number,$n$: principal quantum number]

DifficultJEE MAIN 2025

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The electron energy in a hydrogen atom is given by $E_n = (-2.18 \times 10^{-18})/n^2 \ J$. Calculate the energy required to remove an electron completely from the $n = 2$ orbit. What is the longest wavelength of light in $cm$ that can be used to cause this transition?

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Find out the distance between the $2^{nd}$ and $3^{rd}$ orbit of the $H$-atom $:-$

Medium

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The kinetic energy of electrons emitted, when radiation of frequency $1.0 \times 10^{15} \ Hz$ hits a metal, is $2 \times 10^{-19} \ J$. What is the threshold frequency of the metal (in $Hz$)?
$(h = 6.6 \times 10^{-34} \ Js)$

DifficultTS EAMCET 2024

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$A$ single-electron species has a nuclear charge of $+Ze$,where $Z$ is a constant. The energy required to excite an electron from the $2^{nd}$ Bohr orbit to the $3^{rd}$ Bohr orbit is $47.2 \ eV$. Calculate the value of $Z$.

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For hydrogen-like species,which of the following graphs provides the most appropriate representation of $E$ vs $Z$ plot for a constant $n$?[$E$: Energy of the stationary state,$Z$: atomic number,$n$: principal quantum number]

The electron energy in a hydrogen atom is given by $E_n = (-2.18 \times 10^{-18})/n^2 \ J$. Calculate the energy required to remove an electron completely from the $n = 2$ orbit. What is the longest wavelength of light in $cm$ that can be used to cause this transition?

Find out the distance between the $2^{nd}$ and $3^{rd}$ orbit of the $H$-atom $:-$

The kinetic energy of electrons emitted, when radiation of frequency $1.0 \times 10^{15} \ Hz$ hits a metal, is $2 \times 10^{-19} \ J$. What is the threshold frequency of the metal (in $Hz$)?$(h = 6.6 \times 10^{-34} \ Js)$

$A$ single-electron species has a nuclear charge of $+Ze$,where $Z$ is a constant. The energy required to excite an electron from the $2^{nd}$ Bohr orbit to the $3^{rd}$ Bohr orbit is $47.2 \ eV$. Calculate the value of $Z$.

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For hydrogen-like species,which of the following graphs provides the most appropriate representation of $E$ vs $Z$ plot for a constant $n$?
[$E$: Energy of the stationary state,$Z$: atomic number,$n$: principal quantum number]

The kinetic energy of electrons emitted, when radiation of frequency $1.0 \times 10^{15} \ Hz$ hits a metal, is $2 \times 10^{-19} \ J$. What is the threshold frequency of the metal (in $Hz$)?
$(h = 6.6 \times 10^{-34} \ Js)$