STD 12 - Atoms PYQs: JEE Mains Physics

Showing 1–50 of 131 questions

1. 1. Angular momentum of an electron in a hydrogen atom is \(\dfrac{3h}{\pi}\), then the energy of the electron is _______ eV. 2026 Easy
2. 2. If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is _________ m.
   (Atomic number of gold \(=79\) and \(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9\)in SI units) 2026 Hard
3. 3. In hydrogen atom spectrum, (R is Rydberg's constant):
   A. the maximum wavelength of the radiation of Lyman series is \(\frac{4}{3 R}\)
   B. the Balmer series lies in the visible region of the spectrum
   C. the minimum wavelength of the radiation of Paschen series is \(\frac{9}{R}\)
   D. the minimum wavelength of Lyman series is \(\frac{5}{4 R}\)
   Choose the correct answer from the options given below : 2026 Medium
4. 4. In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because
   A. The size of gold nucleus is very small as compared to the size of gold atom.
   B. Alpha particle and gold nucleus have equal charge.
   C. The impact parameter is minimum for a few alpha particles.
   D. A few alpha particles have very high kinetic energy.
   E. Only a few alpha particles undergo head-on collision with the nuclei.
   Choose the correct answer from the options given below: 2026 Medium
5. 5. 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
6. 6. 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
7. 7. The ratio of momentum of the photons of the \(1^{st}\) and \(2^{nd}\) line of Balmer series of Hydrogen atoms is \(\alpha/\beta\). The possible values of \(\alpha\) and \(\beta\) are:- 2026 Medium
8. 8. The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly __________ nm. 2026 Medium
9. 9. 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
10. 10. 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
11. 11. 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
12. 12. An electron in the hydrogen atom initially in the fourth excited state makes a transition to \(\mathrm{n}^{\text {th }}\) energy state by emitting a photon of energy 2.86 eV. The integer value of \(n\) will be ____. 2025 Easy
13. 13. 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
14. 14. Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of \(\mathrm{Li}^{++}\)ion in its ground state is given by \(\frac{1}{X} a_0\), where \(X=\) _______. (Where \(\mathrm{a}_0\) is the first Bohr's radius.) 2025 Easy
15. 15. Considering Bohr's atomic model for hydrogen atom :
    (A) the energy of H atom in ground state is same as energy of \(\mathrm{He}^{+}\)ion in its first excited state.
    (B) the energy of H atom in ground state is same as that for \(\mathrm{Li}^{++}\)ion in its second excited state.
    (C) the energy of H atom in its ground state is same as that of \(\mathrm{He}^{+}\)ion for its ground state.
    (D) the energy of \(\mathrm{He}^{+}\)ion in its first excited state is same as that for \(\mathrm{Li}^{++}\)ion in its ground state
    Choose the correct answer from the options given below : 2025 Easy
16. 16. 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
17. 17. During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is \(2000 Å\) and it becomes \(6000 Å\) when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is _______. 2025 Medium
18. 18. For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is _______. 2025 Easy
19. 19. 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
20. 20. 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
21. 21. In a hydrogen like ion, the energy difference between the \(2^{\text {nd }}\) excitation energy state and ground is 108.8 eV. The atomic number of the ion is 2025 Medium
22. 22. The frequency of revolution of the electron in Bohr's orbit varies with \(n\), the principal quantum number as _______. 2025 Easy
23. 23. 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
24. 24. 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
25. 25. A hydrogen atom in ground state is given an energy of \(10.2 \mathrm{eV}\). How many spectral lines will be emitted due to transition of electrons? 2024 Medium
26. 26. A particular hydrogen - like ion emits the radiation of frequency \(3 \times 10^{15} \mathrm{~Hz}\) when it makes transition from \(n=2\) to \(n=1\). The frequency of radiation emitted in transition from \(n=3\) to \(n=1\) is \(\frac{x}{9} \times 10^{15} \mathrm{~Hz}\), when \(x=\) = _____. 2024 Hard
27. 27. According to Bohr's theory, the moment of momentum of an electron revolving in \(4^{\text {th }}\) orbit of hydrogen atom is _______. 2024 Hard
28. 28. An electron revolving in \(\mathrm{n}^{\text {th }}\) Bohr orbit has magnetic moment \(\mu_n\). If \(\mu_n\) \(\alpha\) \(n^x\), the value of \(x\) is _______. 2024 Hard
29. 29. 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
30. 30. Given below are two statements : \(Statement\) \(I\) : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model. \(Statement\) \(II\) : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model. In the light of the above statements, choose the most appropriate from the options given below. 2024 Hard
31. 31. Hydrogen atom is bombarded with electrons accelerated through a potential different of \(\mathrm{V}\), which causes excitation of hydrogen atoms. If the experiment is being formed at \(\mathrm{T}=0 \mathrm{~K}\). The minimum potential difference needed to observe any Balmer series lines in the emission spectra will be \(\frac{\alpha}{10} \mathrm{~V}\), where \(\alpha=\) _______. 2024 Hard
32. 32. If Rydberg's constant is \(R\), the longest wavelength of radiation in Paschen series will be \(\frac{\alpha}{7 R}\), where \(\alpha=\)____________ 2024 Hard
33. 33. If the wavelength of the first member of Lyman series of hydrogen is \(\lambda\). The wavelength of the second member will be _______. 2024 Hard
34. 34. In an alpha particle scattering experiment distance of closest approach for the \(\alpha\) particle is \(4.5 \times 10^{-14} \mathrm{~m}\). If target nucleus has atomic number \(80\) , then maximum velocity of \(\alpha\)-particle is _______ \(\times 10^5\) \(\mathrm{m} / \mathrm{s}\) approximately. \(\left(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}\right.\) unit, mass of \(\alpha\) particle \(=\) \(\left.6.72 \times 10^{-27} \mathrm{~kg}\right)\) 2024 Hard
35. 35. Radius of a certain orbit of hydrogen atom is \(8.48\mathring A \). If energy of electron in this orbit is \(\mathrm{E} / \mathrm{x}\), then \(\mathrm{x}=\) _______. (Given \(a_0=0.529 \mathring A, E=\) energy of electron in ground state) 2024 Hard
36. 36. The angular momentum of an electron in a hydrogen atom is proportional to _______. (Where \(\mathrm{r}\) is the radius of orbit of electron) 2024 Hard
37. 37. The longest wavelength associated with Paschen series is _______. (Given \(R_H=1.097 \times 10^7 \mathrm{SI}\) unit) 2024 Hard
38. 38. The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly _______. 2024 Hard
39. 39. The radius of third stationary orbit of electron for Bohr's atom is \(R\). The radius of fourth stationary orbit will be: 2024 Hard
40. 40. 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
41. 41. The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the \(5^{\text {th }}\) excited state of a hydrogen atom is _______. 2024 Hard
42. 42. The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is _______. 2024 Hard
43. 43. The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is \(915\)\(A\). The longest wavelength of spectral lines in the Balmer series will be _______ \(A\). 2024 Hard
44. 44. When a hydrogen atom going from \(\mathrm{n}=2\) to \(\mathrm{n}=1\) emits a photon, its recoil speed is \(\frac{\mathrm{x}}{5} \mathrm{~m} / \mathrm{s}\). Where \(\mathrm{x}=\) _______. (Use : mass of hydrogen atom\(\left.=1.6 \times 10^{-27 /} \ \mathrm{kg}\right)\) 2024 Hard
45. 45. A \(12.5\,eV\) electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be: 2023 Hard
46. 46. A light of energy \(12.75 \;eV\) is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is \(\frac{x}{\pi} \times 10^{-17} \;eVs\). The value of \(x\) is \(........\) (use \(h=4.14 \times 10^{-15} \;eVs , c=3 \times 10^8\;\left.ms ^{-1}\right)\) 2023 Medium
47. 47. A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is \(x \times 10^{15}\,Hz\). The value of \(x\) is (Given \(h =4.25 \times 10^{-15}\,eVs\) ) 2023 Medium
48. 48. A photon is emitted in transition from \(n =4\) to \(n =1\) level in hydrogen atom. The corresponding wavelength for this transition is \(.........\,nm\) \(\text { (given, } h =4 \times 10^{-15} eVs \text { ) : }\) 2023 Medium
49. 49. 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
50. 50. An atom absorbs a photon of wavelength \(500\,nm\) and emits another photon of wavelength \(600\,nm\). The net energy absorbed by the atom in this process is \(n \times 10^{-4}\,eV\). The value of \(n\) is ............ [Assume the atom to be stationary during the absorption and emission process] \(\left(\right.\)Take \(h =6.6 \times 10^{-34}\,Js\) and \(\left.c =3 \times 10^8\,m / s \right)\) 2023 Medium

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