Bohr's Model

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JEE Advanced 2026

$X^{a +}$ and $Y^{b +}$ are hydrogen-like species. The wavelength of light absorbed during the transition between the states with principal quantum numbers $n = 1$ and $n = 2$ of $X^{a +}$ is $λ$ . The wavelength of light absorbed during the transition between the states with principal quantum numbers $n = 2$ and $n = 4$ of $Y^{b +}$ is $9 λ$ . The lowest possible value of $(a + b)$ is _____.

JEE Advanced 2019

Comprehension Passage

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following List-I contains some quantities for the

n^{th}

orbit of the atom and List-II contains options showing how they depend on

n

. \begin{array}{ll} \textbf{List-I} & \textbf{List-II} \\ \text{(I) Radius of the } n^{\text{th}} \text{ orbit} & \text{(P) } \propto n^{-2} \\ \text{(II) Angular momentum of the electron in the } n^{\text{th}} \text{ orbit} & \text{(Q) } \propto n^{-1} \\ \text{(III) Kinetic energy of the electron in the } n^{\text{th}} \text{ orbit} & \text{(R) } \propto n^0 \\ \text{(IV) Potential energy of the electron in the } n^{\text{th}} \text{ orbit} & \text{(S) } \propto n^1 \\ & \text{(T) } \propto n^2 \\ & \text{(U) } \propto n^{1/2} \end{array}

Question 1:

Which of the following options has the correct combination considering List-I and List-II ?

Which of the following options has the correct combination considering List-I and List-II ?

The figure below is the plot of potential energy versus internuclear distance ( $d$ ) of H $_{2}$ molecule in the electronic ground state. What is the value of the net potential energy $E_{0}$ (as indicated in the figure) in kJ mol $^{- 1}$ , for $d = d_{0}$ at which the electron-electron repulsion and the nucleus-nucleus repulsion energies are absent? As reference, the potential energy of H atom is taken as zero when its electron and the nucleus are infinitely far apart. [Use Avogadro constant as $6.023 \times 1 0^{23} mol^{- 1}$ .]

JEE Advanced 2023

LEVELJEE Main

For $He^{+}$ , a transition takes place from the orbit of radius $105.8 pm$ to the orbit of radius $26.45 pm$ . The wavelength (in nm) of the emitted photon during the transition is ______. [Use: Bohr radius, $a = 52.9 pm$ Rydberg constant, $R_{H} = 2.2 \times 1 0^{- 18} J$ Planck's constant, $h = 6.6 \times 1 0^{- 34} J s$ Speed of light, $c = 3 \times 1 0^{8} m s^{- 1}$ ]

JEE Main 2021

LEVELJEE Main

According to Bohr's atomic theory, I. kinetic energy of electron is $\propto \frac{Z ^{2}}{n ^{2}}$ II. the product of velocity ( $v$ ) of electron and principal quantum number ( $n$ ), ' $v n$ ' $\propto Z^{2}$ . III. frequency of revolution of electron in an orbit is $\propto \frac{Z ^{3}}{n ^{3}}$ IV. coulombic force of attraction on the electron is $\propto \frac{Z ^{3}}{n ^{4}}$ Choose the most appropriate answer from the options given below.

Given below are two statements. Statement I: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in positive charges on the nucleus as there is no strong hold on the electron by the nucleus. Statement II: According to Bohr's model of an atom, qualitatively the magnitude of velocity of electron increases with decrease in principal quantum number. In the light of the above statements, choose the most appropriate answer from the options given below.

(A)

Both statement I and statement II are false.

(B)

Both statement I and statement II are true.

(C)

Statement I is false but statement II is true.

(D)

Statement I is true but statement II is false.

JEE Main 2019

LEVELJEE Main

The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are

The region in the electromagnetic spectrum where the Balmer series lines appear is

The frequency of light emitted for the transition $n = 4$ to $n = 2$ of $He^{+}$ is equal to the transition in H atom corresponding to which of the following?

(A)

n = 3 to n = 1

(B)

n = 2 to n = 1

(C)

n = 3 to n = 2

(D)

n = 4 to n = 3

JEE Main 2019

LEVELJEE Main

Heat treatment of muscular pain involves radiation of wavelength of about $900 nm$ . Which spectral line of H-atom is suitable for this purpose? [ $R_{H} = 1 \times 1 0^{5} cm^{- 1}$ , $h = 6.6 \times 1 0^{- 34} Js, c = 3 \times 1 0^{8} ms^{- 1}$ ]

(A)

Paschen,

5 \to 3

(B)

Paschen,

\infty \to 3

(C)

Lyman,

\infty \to 1

(D)

Balmer,

\infty \to 2

JEE Main 2017

LEVELJEE Main

The radius of the second Bohr orbit for hydrogen atom is (Planck's constant $(h) = 6.6262 \times 1 0^{- 34} Js$ ; mass of electron $= 9.1091 \times 1 0^{- 31} kg$ ; charge of electron $(e) = 1.60210 \times 1 0^{- 19} C$ ; permitivity of vacuum $(ϵ_{0}) = 8.854185 \times 1 0^{- 12} kg^{- 1} m^{- 3} A^{2}$ )

(A)

1.65 \overset{˚}{A}

(B)

4.76 \overset{˚}{A}

(C)

0.529 \overset{˚}{A}

(D)

2.12 \overset{˚}{A}

JEE Main 2019

LEVELJEE Main

For any given series of spectral lines of atomic hydrogen, let $Δ \overset{ν}{ˉ} = \overset{ν}{ˉ}_{m a x} - \overset{ν}{ˉ}_{m i n}$ be the difference in maximum and minimum frequencies in $cm^{- 1}$ . The ratio $Δ \overset{ν}{ˉ}_{Lyman} /Δ \overset{ν}{ˉ}_{Balmer}$ is

The ground state energy of hydrogen atom is $- 13.6 eV$ . The energy of second excited state of $He^{+}$ ion in eV is

(A)

- 54.4

(B)

- 3.4

(C)

- 6.04

(D)

- 27.2

JEE Main 2013

LEVELJEE Main

Energy of an electron is given by $E = - 2.178 \times 1 0^{- 18} J (\frac{Z ^{2}}{n ^{2}})$ . Wavelength of light required to excite an electron in an hydrogen atom from level $n = 1$ to $n = 2$ will be ( $h = 6.62 \times 1 0^{- 34} J s$ and $c = 3.0 \times 1 0^{8} ms^{- 1}$ )

(A)

1.214 \times 1 0^{- 7} m

(B)

2.816 \times 1 0^{- 7} m

(C)

6.500 \times 1 0^{- 7} m

(D)

8.500 \times 1 0^{- 7} m

JEE Main 2020

LEVELJEE Main

The radius of the second Bohr orbit in terms of the Bohr radius, $a_{0}$ , in $Li^{2 +}$ is

(A)

\frac{2 a _{0}}{3}

(B)

\frac{4 a _{0}}{3}

(C)

\frac{4 a _{0}}{9}

(D)

\frac{2 a _{0}}{9}

JEE Main 2020

LEVELJEE Main

For the Balmer series in the spectrum of H atom, $\overset{ν}{ˉ} = R_{H} {\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}}}$ , the correct statements among (I) to (IV) are : (I) As wavelength decreases, the lines in the series converge (II) The integer $n_{1}$ is equal to 2 (III) The lines of longest wavelength corresponds to $n_{2} = 3$ (IV) The ionisation energy of hydrogen can be calculated from wave number of these lines

Which of the following is the energy of a possible excited state of hydrogen?

(A)

+ 13.6 eV

(B)

- 6.8 eV

(C)

- 3.4 eV

(D)

+ 6.8 eV

JEE Main 2019

LEVELJEE Main

For emission line of atomic hydrogen from $n_{i} = 8$ to $n_{f} = n$ , the plot of wave number ( $\overset{ν}{ˉ}$ ) against $(\frac{1}{n ^{2}})$ will be (The Rydberg constant, $R_{H}$ is in wave number unit)

- R_{H}

(C)

linear with slope

R_{H}

(D)

linear with intercept

- R_{H}

JEE Main 2021

LEVELJEE Main

The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to $\frac{h ^{2}}{x m a _{0}^{2}}$ . The value of $10 x$ is ……… . ( $a_{0}$ is radius of Bohr's orbit) (Nearest integer) [Given, $π = 3.14$ ]

JEE Main 2021

LEVELJEE Main

Given below are two statements. Statement I Bohr's theory accounts for the stability and line spectrum of $Li^{+}$ ion. Statement II Bohr's theory was unable to explain the splitting of spectral lines in the presence of a magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below :

(A)

Both statements I and II are true.

(B)

Statement I is false but statement II is true.

(C)

Both statements I and II are false.

(D)

Statement I is true but statement II is false.

JEE Main 2020

LEVELJEE Main

The difference between the radii of 3rd and 4th orbits of $Li^{2 +}$ is $Δ R_{1}$ . The difference between the radii of 3rd and 4th orbits of $He^{+}$ is $Δ R_{2}$ . Ratio $Δ R_{1} : Δ R_{2}$ is

(A)

3 : 2

(B)

8 : 3

(C)

2 : 3

(D)

3 : 8

JEE Main 2020

LEVELJEE Main

The shortest wavelength of H atom in the Lyman series is $λ_{1}$ . The longest wavelength in the Balmer series of $He^{+}$ is

(A)

\frac{36 λ _{1}}{5}

(B)

\frac{5 λ _{1}}{9}

(C)

\frac{9 λ _{1}}{5}

(D)

\frac{27 λ _{1}}{5}

Comprehension Passage

Which of the following options has the correct combination considering List-I and List-II ?

Which of the following options has the correct combination considering List-I and List-II ?

The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are

The region in the electromagnetic spectrum where the Balmer series lines appear is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The frequency of light emitted for the transition n=4 to n=2 of He+ is equal to the transition in H atom corresponding to which of the following?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The ground state energy of hydrogen atom is −13.6 eV. The energy of second excited state of He+ ion in eV is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The radius of the second Bohr orbit in terms of the Bohr radius, a0​, in Li2+ is

Which of the following is the energy of a possible excited state of hydrogen?

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For emission line of atomic hydrogen from ni​=8 to nf​=n, the plot of wave number (νˉ) against (n21​) will be (The Rydberg constant, RH​ is in wave number unit)

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The difference between the radii of 3rd and 4th orbits of Li2+ is ΔR1​. The difference between the radii of 3rd and 4th orbits of He+ is ΔR2​. Ratio ΔR1​:ΔR2​ is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The shortest wavelength of H atom in the Lyman series is λ1​. The longest wavelength in the Balmer series of He+ is

The frequency of light emitted for the transition $n = 4$ to $n = 2$ of $He^{+}$ is equal to the transition in H atom corresponding to which of the following?

The ground state energy of hydrogen atom is $- 13.6 eV$ . The energy of second excited state of $He^{+}$ ion in eV is

The radius of the second Bohr orbit in terms of the Bohr radius, $a_{0}$ , in $Li^{2 +}$ is

For emission line of atomic hydrogen from $n_{i} = 8$ to $n_{f} = n$ , the plot of wave number ( $\overset{ν}{ˉ}$ ) against $(\frac{1}{n ^{2}})$ will be (The Rydberg constant, $R_{H}$ is in wave number unit)

The difference between the radii of 3rd and 4th orbits of $Li^{2 +}$ is $Δ R_{1}$ . The difference between the radii of 3rd and 4th orbits of $He^{+}$ is $Δ R_{2}$ . Ratio $Δ R_{1} : Δ R_{2}$ is

The shortest wavelength of H atom in the Lyman series is $λ_{1}$ . The longest wavelength in the Balmer series of $He^{+}$ is