Bohr's Model of Hydrogen Atom PYQs: JEE Mains Physics

Showing 1–22 of 22 questions

1. 1. In the hydrogen atom, the electron makes a transition from the higher orbit (\(i\)) to a lower orbit (\(f\)). The ratio of the radius of the orbits in given by \(r_i : r_f = 16 : 4\). The wavelength of photon emitted due to this transition is _____ nm.
   (Given Rydberg constant \(= 1.0973 \times 10^7\) /m) 2026 Hard
2. 2. The energy of an electron in an orbit of the Bohr's atom is \(-0.04 E _0 eV\) where \(E _0\) is the ground state energy. If \(L\) is the angular momentum of the electron in this orbit and h is the Planck's constant, then \(\frac{2 \pi L}{ h }\) is _________ : 2026 Easy
3. 3. Two electrons are moving in orbits of two hydrogen like atoms with speeds \(3 \times 10^5 m / s\) and \(2.5 \times 10^5 m / s\) respectively. If the radii of these orbits are nearly same then the possible order of energy states are _________ respectively. 2026 Hard
4. 4. Using Bohr's model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the \(2^{\text{nd}}\) and \(4^{\text{th}}\) orbits of hydrogen atom _______. 2026 Medium
5. 5. An electron in the ground state of the hydrogen atom has the orbital radius of \(5.3 \times 10^{-11} \mathrm{~m}\) while that for the electron in third excited state is \(8.48 \times 10^{-10} \mathrm{~m}\). The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is _______. 2025 Easy
6. 6. An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is : 2025 Medium
7. 7. Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius \(5^{\text {th}}\) orbit of the electron in \(\mathrm{Li}^{2+}\) and \(\mathrm{He}^{+}\) is _______. 2025 Easy
8. 8. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
   Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only.
   Reason R : The formulation of Bohr model does not include repulsive force between electrons.
   In the light of the above statements, choose the correct answer from the options given below : 2025 Easy
9. 9. Given below are two statements :
   Statement (I) : The dimensions of Planck's constant and angular momentum are same.
   Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.
   In the light of the above statements, choose the most appropriate answer from the options given below : 2025 Medium
10. 10. The frequency of revolution of the electron in Bohr's orbit varies with \(n\), the principal quantum number as _______. 2025 Easy
11. 11. A electron of hydrogen atom on an excited state is having energy \(E_n=-0.85 \mathrm{eV}\). The maximum number of allowed transitions to lower energy level is _______. 2024 Hard
12. 12. A hydrogen atom changes its state from \(n=3\) to \(\mathrm{n}=2\). Due to recoil, the percentage change in the wave length of emitted light is approximately \(1 \times 10^{-\mathrm{n}}\). The value of \(\mathrm{n}\) is _______. [Given \(\mathrm{Rhc}=13.6 \mathrm{eV}, \mathrm{hc}=1242 \mathrm{eV} \mathrm{nm}\), \(\mathrm{h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}\), mass of the hydrogen atom \(\left.=1.6 \times 10^{-27} \mathrm{~kg}\right]\) 2024 Hard
13. 13. An electron rotates in a circle around a nucleus having positive charge \(\mathrm{Ze}\). Correct relation between total energy ( \(E\) ) of electron to its potential energy \((U)\) is _______. 2024 Hard
14. 14. The radius of third stationary orbit of electron for Bohr's atom is \(R\). The radius of fourth stationary orbit will be what? 2024 Medium
15. 15. A small particle of mass \(m\) moves in such a way that its potential energy \(U=\frac{1}{2} m \omega^2 r ^2\) where \(\omega\) is constant and \(r\) is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of \(n^{\text {th }}\) orbit will be proportional to. 2023 Medium
16. 16. Speed of an electron in Bohr's \(7^{\text {th }}\) orbit for Hydrogen atom is \(3.6 \times 10^6\,m / s\). The corresponding speed of the electron in \(3^{\text {rd }}\) orbit, in \(m / s\) is \(........\times 10^6\) 2023 Medium
17. 17. The angular momentum for the electron in Bohr's orbit is \(L\). If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be 2023 Medium
18. 18. The radius of \(2^{\text {nd }}\) orbit of \(He ^{+}\)of Bohr's model is \(r _1\) and that of fourth orbit of \(Be ^{3+}\) is represented as \(r _2\). Now the ratio \(\frac{r_2}{r_1}\) is \(x : 1\). The value of \(x\) is ......... 2023 Medium
19. 19. The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of the third orbit will be 2023 Medium
20. 20. The radius of electron's second stationary orbit in Bohr's atom is \(R\). The radius of \(3 rd\) orbit will be \(.........R\) 2023 Easy
21. 21. The radius of fifth orbit of the \(L ^{++}\)is \(.........\times 10^{-12}\,m\). Take : radius of hydrogen atom \(=0.51 \mathring A\) 2023 Medium
22. 22. In the Bohr 's model of hydrogen-like atom the force between the nucleus and the electron is modified as \(F = \frac{{{e^2}}}{{4\pi {\varepsilon _0}}}\left( {\frac{1}{{{r^2}}} + \frac{\beta }{{{r^3}}}} \right)\), where \(\beta \) is a constant. For this atom, the radius of the \(n^{th}\) orbit in terms of the Bohr radius \(\left( {{a_0} = \,\frac{{{\varepsilon _0}{h^2}}}{{m\pi {e^2}}}} \right)\) is 2013 Hard

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