MHT-CET PYQ’s 2024 - STRUCTURE OF ATOMS AND NUCLEI

STRUCTURE OF ATOMS AND NUCLEI

1. The angular momentum of the electron in the third Bohr orbit of a hydrogen atom is ‘l’. Its angular momentum in the fourth Bohr orbit is:

[MHT-CET 2024, May 5, Shift 2]

• (1) 4l
• (2) \(\frac{4}{3}\)l
• (3) \(\frac{5}{4}\)l
• (4) \(\frac{3}{3}\)l

2. The ratio of the radius of the first Bohr orbit to that of the second Bohr orbit of the orbital electron is:

[MHT-CET 2024, May 3, Shift 2]

• (1) 4:1
• (2) 2:1
• (3) 1:4
• (4) 1:2

3. The radius of the innermost orbit of a hydrogen atom is 5.3 × 10^-11 m. The radius of the fourth allowed orbit of the hydrogen atom is:

[MHT-CET 2024, May 2, Shift 1]

• (1) 8.48 Å
• (2) 2.12 Å
• (3) 4.77 Å
• (4) 0.53 Å

4. In a hydrogen atom in its ground state, the first Bohr orbit has radius r₁. The electron’s orbital speed becomes one-third when the atom is raised to one of its excited states. The radius of the orbit in that excited state is:

[MHT-CET 2024, May 11, Shift 2]

• (1) \( 3r_1 \)
• (2) \( 4r_1 \)
• (3) \( 9r_1 \)
• (4) \( 16r_1 \)

5. The ratio of energies of photons produced due to the transition of an electron of a hydrogen atom from its (a) second to first energy level and (b) highest energy level to the second level is:

[MHT-CET 2024, May 11, Shift 1]

• (1) 1:3
• (2) 1:2
• (3) 3:1
• (4) 4:1

6. In a hydrogen atom, if V_n and V_p are orbital velocities in the n^th and p^th orbit respectively, then the ratio V_p : V_n is:

[MHT-CET 2024, May 9, Shift 2]

• (1) \( p : n \)
• (2) \( n : p \)
• (3) \( p^2 : n^2 \)
• (4) \( n^2 : p^2 \)

7. In the Bohr model of the hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If ‘r₀’ is the radius of the ground state orbit, ‘m’ is the mass, ‘e’ is the charge on the electron, and ‘ε₀’ is the permittivity of vacuum, the speed of the electron is:

[MHT-CET 2024, May 10, Shift 2]

• (1) zero
• (2) \( \frac{e}{\sqrt{\epsilon_0 r_0 m }} \)
• (3) \( \frac{e}{\sqrt{4 \pi \epsilon_0 r_0 m}} \)
• (4) \( \frac{\sqrt{4 \pi \epsilon_0 r_0 m}}{e} \)

8. Acceleration of an electron in the first Bohr’s orbit is proportional to (m = mass of electron, r = radius of the orbit, h = Planck’s constant):

[MHT-CET 2024, May 15, Shift 2]

• (1) \( \frac{m^3 r^3}{h^2} \)
• (2) \( \frac{h^2}{m^2 r^3} \)
• (3) \( \frac{h^2}{m r^3} \)
• (4) \( \frac{m r^3}{h^2} \)

9. Using Bohr’s model, the orbital period of an electron in a hydrogen atom in the nth orbit is (m = mass of electron, h = Planck’s constant, e = electronic charge, ε₀ = permittivity of free space):

[MHT-CET2024,May10,Shift1]

• (1) \( \frac{2 \epsilon_0^2 n^2 h^2}{m e^4} \)
• (2) \( \frac{4 \epsilon_0^2 n^2 h^2}{m e^2} \)
• (3) \( \frac{4 \epsilon_0^2 n^3 h^3}{m e^4} \)
• (4) \( \frac{4 \epsilon n^2 h^2}{ \pi m e^2} \)

10. Radius of the first orbit in a hydrogen atom is ‘a₀’. Then, the de-Broglie wavelength of an electron in the third orbit is:

[MHT-CET 2024, May 10, Shift 2]

• (1) 3πa₀
• (2) 6πa₀
• (3) 9πa₀
• (4) 12πa₀

11. Which of the following statements about the Bohr model of the hydrogen atom is false?

[MHT-CET 2024, May 2, Shift 2]

• (1) Acceleration of the electron in n = 2 orbit is less than that in n = 1 orbit
• (2) Angular momentum of the electron in n = 2 orbit is more than that in n = 1 orbit
• (3) Kinetic energy of the electron in n = 2 orbit is less than that in n = 1 orbit
• (4) Potential energy of the electron in n = 2 orbit is less than that in n = 1 orbit

12. When a hydrogen atom is raised from the ground state to an excited state:

[MHT-CET 2024, May 9, Shift 1]

• (1) Potential energy increases and kinetic energy decreases
• (2) Potential energy decreases and kinetic energy increases
• (3) Both kinetic energy and potential energy increase
• (4) Both kinetic energy and potential energy decrease

13. If the ionization energy for the hydrogen atom is 13.6 eV, then the energy required to excite it from the ground state to the next higher state is nearly:

[MHT-CET 2024, May 10, Shift 1]

• (1) 10.2 eV
• (2) 13.6 eV
• (3) -10.2 eV
• (4) -3.4 eV

14. In the second orbit of a hydrogen atom, the energy of an electron is ‘E’. In the third orbit of a helium atom, the energy of the electron will be (atomic number of helium = 2):

[MHT-CET 2024, May 16, Shift 2]

• (1) \( \frac{4E}{9} \)
• (2) \( \frac{4E}{3} \)
• (3) \( \frac{16E}{9} \)
• (4) \( \frac{16E}{3} \)

15. In the third orbit of a hydrogen atom, the energy of an electron is ‘E’. In the fifth orbit of helium (Z = 2), the energy of the electron will be:

[MHT-CET 2024, May 2, Shift 1]

• (1) \( \frac{25E}{36} \)
• (2) \( \frac{36E}{25} \)
• (3) \( \frac{3E}{5} \)
• (4) \( \frac{5E}{3} \)

16. An electron of a stationary hydrogen atom passes from the fifth energy level to the ground level. The velocity that the atom acquires as a result of photo emission is (m = mass of electron, R = Rydberg’s constant, h = Planck’s constant):

[MHT-CET 2024, May 2, Shift 2]

• (1) \( \frac{24Rh}{25m} \)
• (2) \( \frac{25Rh}{24m} \)
• (3) \( \frac{25m}{24Rh} \)
• (4) \( \frac{24m}{25Rh} \)

17. A diatomic molecule has a moment of inertia ‘I’. By applying Bohr’s quantization condition, its rotational energy in the nth level is [n ≥ 1] (h = Planck’s constant):

[MHT-CET 2024, May 3, Shift 2]

• (1) \( \frac{1}{n^2} \) ( \( \frac{h^2}{8 \pi^2 I} \) )
• (2) \( \frac{1}{n^2} \) ( \( \frac{h^2}{8 \pi^2 I} \) )
• (3) n ( \( \frac{h^2}{8 \pi^2 I} \) )
• (4) \( n^2 \) ( \( \frac{h^2}{8 \pi^2 I} \) )

18. When an electron orbiting in a hydrogen atom in its ground state jumps to a higher excited state, the de-Broglie wavelength associated with it:

[MHT-CET 2024, May 16, Shift 1]

• (1) will become zero
• (2) will remain the same
• (3) will decrease
• (4) will increase

19. When the electron orbiting in a hydrogen atom in its ground state moves to the third excited state, the de-Broglie wavelength associated with it:

[MHT-CET 2024, May 3, Shift 2]

• (1) becomes zero
• (2) remains unchanged
• (3) will decrease
• (4) will increase

20. The spectral series observed for the hydrogen atom found in the visible region is:

[MHT-CET 2024, May 9, Shift 2]

• (1) Lyman
• (2) Balmer
• (3) Paschen
• (4) Brackett

21. If ‘λ₁’ and ‘λ₂’ are the wavelengths of the first line of the Lyman and Paschen series respectively, then λ₂ : λ₁ is:

[MHT-CET 2024, May 3, Shift 1]

• (1) 3 : 1
• (2) 30 : 1
• (3) 50 : 7
• (4) 108 : 7

22. The ratio of the minimum wavelengths of the Lyman and Balmer series is:

[MHT-CET 2024, May 4, Shift 2]

• (1) 1.25
• (2) 0.25
• (3) 5
• (4) 10

23. According to Bohr’s theory of the hydrogen atom, the ratio of the maximum and minimum wavelengths of the Lyman series is:

[MHT-CET 2024, May 9, Shift 1]

• (1) 3 : 4
• (2) 4 : 3
• (3) 2 : 5
• (4) 5 : 2

24. In a hydrogen atom, the ratio of the shortest wavelength in the Balmer series to that in the Paschen series is:

[MHT-CET 2024, May 5, Shift 2]

• (1) 9 : 4
• (2) 3 : 1
• (3) 4 : 9
• (4) 1 : 3

25. For a hydrogen atom, ‘λ₁’ and ‘λ₂’ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in the figure. The ratio of ‘λ₁’ and ‘λ₂’ is \( \frac{x}{32} \). The value of ‘x’ is:

 

[MHT-CET 2024, May 4, Shift 1]

• (1) 3
• (2) 9
• (3) 27
• (4) 81

26. Frequency of the series limit of the Balmer series of a hydrogen atom of Rydberg’s constant ‘R’ and velocity of light ‘C’ is:

[MHT-CET 2024, May 16,Shift 1]

• (1) \( \frac{RC}{4} \)
• (2) \( RC \)
• (3) \( \frac{4}{RC} \)
• (4) \( 4RC \)

 

27. If M₀ is the mass of an oxygen isotope ₈O¹⁷ and M_p and M_N are the mass of a proton and neutron respectively, then the nuclear binding energy of the isotope is:

[MHT-CET 2024, May 16, Shift 1]

• (1) M₀C²
• (2) (M₀ – 8M_P)C²
• (3) (M₀ – 17M_N)C²
• (4) (M₀ – 8M_P – 9M_N)C²

28. If ‘T’ is the half-life of a radioactive substance, then its instantaneous rate of change of activity is proportional to:

[MHT-CET 2024, May 11, Shift 1]

• (1) \( T \)
• (2) \( T^{-2} \)
• (3) \( T^{+2} \)
• (4) \( T^{-1} \)

29. In the uranium radioactive series, the initial nucleus is \( ^{238}_{92}\text{U} \) and the final nucleus is \( ^{206}_{82}\text{Pb} \). When uranium decays into lead, the number of α-particles and β-particles emitted are:

[MHT-CET 2024, May 03, Shift 1]

• (1) 4α, 5β
• (2) 5α, 3β
• (3) 6α, 7β
• (4) 8α, 6β

30. In the given reaction _ZX^A \( \to \) _Z+1Y^A \( \to \) _Z-1A-4^A \( \to \) _Z-1A-4^A, radioactive radiations are emitted in the sequence:

[MHT-CET 2024, May 15, Shift 2]

• (1) α, β, γ
• (2) β, α, γ
• (3) γ, α, β
• (4) β, γ, α

31. Half-lives of two radioactive elements A and B are 30 minutes and 60 minutes respectively. Initially, the samples have equal numbers of nuclei. After 120 minutes, the ratio of the decayed numbers of nuclei of B to that of A will be:

[MHT-CET 2024, May 4, Shift 2]

• (1) 1 : 15
• (2) 1 : 4
• (3) 4 : 5
• (4) 5 : 4

32. Two radioactive substances A and B have decay constants ‘5λ’ and ‘λ’, respectively. At t = 0, they have the same number of nuclei. The ratio of the number of nuclei of A to those of B will be \( (\frac{1}{e})^2 \) after a time interval:

[MHT-CET 2024, May 16, Shift 2]

• (1) \( \frac{1}{4\lambda} \)
• (2) \( 4\lambda \)
• (3) \( 2\lambda \)
• (4) \( \frac{1}{2\lambda} \)

We will post the solution to this paper in 24 hours. The download link will be activated at that time. In the meantime, students are encouraged to attempt the questions on their own and use the comments section to discuss and collaborate with each other.

Download solution here.