JEE Main - Energy levels and hydrogen spectrum Online Test (MCQ Quiz)

1. What is the energy of the ground state of the hydrogen atom according to the Bohr model?

A) -13.6 eV B) 0 eV C) 13.6 eV D) 1.6 eV

2. Which quantum number determines the energy level of an electron in a hydrogen atom?

A) Azimuthal quantum number (l) B) Spin quantum number (s) C) Magnetic quantum number (ml) D) Principal quantum number (n)

3. The energy of an electron in the nth orbit of a hydrogen atom is given by the formula:

A) En = -13.6 / n eV B) En = -13.6 * n eV C) En = 13.6 / n eV D) En = 13.6 * n eV

4. What is the energy difference between the n=2 and n=1 levels in a hydrogen atom?

A) 10.2 eV B) 3.4 eV C) 1.51 eV D) 0.85 eV

5. The spectral lines in the Lyman series of hydrogen correspond to transitions from higher energy levels to which level?

A) n = 1 B) n = 2 C) n = 3 D) n = 4

6. Which series in the hydrogen spectrum lies in the ultraviolet region?

A) Lyman series B) Balmer series C) Paschen series D) Brackett series

7. The Balmer series of hydrogen spectrum lies in which region of the electromagnetic spectrum?

A) Infrared B) Visible C) Ultraviolet D) X-ray

8. Transitions from n=3 to n=2 in hydrogen atom result in a spectral line belonging to which series?

A) Lyman series B) Balmer series C) Paschen series D) Brackett series

9. The Paschen series of hydrogen spectrum corresponds to transitions ending at which principal quantum number?

A) n = 1 B) n = 2 C) n = 3 D) n = 4

10. What is the energy of the electron in the first excited state of hydrogen atom?

A) -13.6 eV B) -3.4 eV C) 0 eV D) 13.6 eV

11. The ionization energy of hydrogen atom is the energy required to excite the electron from:

A) n=1 to n=2 B) n=1 to n=3 C) n=1 to n=infinity D) n=2 to n=infinity

12. The radius of the nth orbit of a hydrogen atom is proportional to:

A) n B) n^2 C) 1/n D) 1/n^2

13. If the electron in a hydrogen atom jumps from n=4 to n=1, it emits a photon of energy corresponding to which series?

A) Lyman series B) Balmer series C) Paschen series D) Brackett series

14. The Pfund series in the hydrogen spectrum corresponds to transitions ending at which principal quantum number?

A) n = 3 B) n = 4 C) n = 5 D) n = 6

15. What is the wavelength of the photon emitted when an electron in a hydrogen atom transitions from n=3 to n=2?

A) 656 nm B) 486 nm C) 434 nm D) 122 nm

16. The longest wavelength line in the Lyman series is obtained when the electron transitions from:

A) n=2 to n=1 B) n=3 to n=1 C) n=infinity to n=1 D) n=4 to n=1

17. The energy levels of a hydrogen-like atom are given by En = -13.6 * Z^2 / n^2 eV, where Z is the atomic number. For Helium ion (He+), Z is:

A) 1 B) 2 C) 3 D) 4

18. The shortest wavelength line in the Balmer series is obtained when the electron transitions from:

A) n=2 to n=3 B) n=3 to n=2 C) n=infinity to n=2 D) n=4 to n=2

19. Rydberg's formula for the wavelength of spectral lines in hydrogen is given by 1/λ = R * (1/n_f^2 - 1/n_i^2), where R is the Rydberg constant. The value of R is approximately:

A) 1.1 x 10^7 m^-1 B) 1.1 x 10^9 m^-1 C) 1.1 x 10^5 m^-1 D) 1.1 x 10^11 m^-1

20. What is the angular momentum of an electron in the ground state (n=1) of a hydrogen atom?

A) h/2π B) h C) 2h/2π D) 0

21. The spectral lines of the Brackett series occur in which region of the electromagnetic spectrum?

A) Visible B) Ultraviolet C) Infrared D) Microwave

22. If an electron in a hydrogen atom moves from a higher energy level to a lower energy level, it:

A) Absorbs a photon B) Emits a photon C) Remains in the same energy level D) Changes its charge

23. The energy required to remove the electron from the n=1 state of hydrogen atom is called:

A) Excitation energy B) Ionization energy C) Binding energy D) Both (b) and (c)

24. The energy of the second excited state (n=3) of hydrogen atom is:

A) -13.6 eV B) -3.4 eV C) -1.51 eV D) -0.85 eV

25. In the hydrogen spectrum, the transition from n=5 to n=2 gives rise to a spectral line in which series?

A) Lyman series B) Balmer series C) Paschen series D) Brackett series

26. The frequency of emitted radiation when an electron transitions from a higher energy state E_i to a lower energy state E_f is given by:

A) f = (E_i - E_f) / h B) f = h / (E_i - E_f) C) f = (E_i + E_f) / h D) f = h / (E_i + E_f)

27. Which of the following transitions in a hydrogen atom will emit the highest energy photon?

A) n=2 to n=1 B) n=3 to n=2 C) n=4 to n=3 D) n=5 to n=4

28. The radius of the Bohr orbit is quantized because:

A) Energy is quantized B) Angular momentum is quantized C) Velocity is quantized D) Charge is quantized

29. The maximum number of spectral lines that can be emitted by a hydrogen atom when an electron is excited to the n=4 level is:

A) 3 B) 4 C) 5 D) 6

30. The energy of a photon emitted during a transition from n=2 to n=1 in hydrogen atom is approximately:

A) 1.6 eV B) 3.4 eV C) 10.2 eV D) 13.6 eV

31. The Bohr model is applicable to:

A) Multi-electron atoms B) Single-electron atoms/ions C) Molecules D) Solids

32. The energy levels of a hydrogen atom are discrete because:

A) The electron is confined to the atom B) The electron's de Broglie wavelength fits an integer number of times around the orbit C) The nucleus is positively charged D) The electron has wave-particle duality

33. The shortest wavelength in the Paschen series of the hydrogen spectrum corresponds to the transition from:

A) n=4 to n=3 B) n=5 to n=3 C) n=infinity to n=3 D) n=6 to n=3

34. The ratio of the radius of the first Bohr orbit to the radius of the second Bohr orbit in hydrogen atom is:

A) 1:2 B) 1:4 C) 1:8 D) 2:1

35. When an electron in a hydrogen atom is excited from n=1 to n=infinity, the energy absorbed is:

A) 13.6 eV B) 10.2 eV C) 3.4 eV D) 0 eV

36. The spectral lines in the Brackett series correspond to transitions ending at which principal quantum number?

A) n = 2 B) n = 3 C) n = 4 D) n = 5

37. If the energy of an electron in a hydrogen atom is -0.85 eV, it is in the energy level n equal to:

A) 1 B) 2 C) 3 D) 4

38. The work done to move an electron from n=1 to n=2 in a hydrogen atom is:

A) 10.2 eV B) -10.2 eV C) 3.4 eV D) -3.4 eV

39. The longest wavelength line in the Balmer series corresponds to the transition from:

A) n=3 to n=2 B) n=4 to n=2 C) n=5 to n=2 D) n=infinity to n=2

40. In the hydrogen spectrum, the transition from n=6 to n=2 gives a spectral line belonging to which series?

A) Lyman series B) Balmer series C) Paschen series D) Brackett series

41. The energy of the electron in the nth orbit of hydrogen atom is proportional to:

A) n B) 1/n C) n^2 D) 1/n^2

42. The number of spectral lines emitted when an electron jumps from n=5 to n=1 in a hydrogen atom is:

A) 4 B) 5 C) 10 D) 15

43. The energy of the photon emitted when an electron transitions from n=3 to n=1 in a hydrogen atom is:

A) 1.51 eV B) 12.09 eV C) 13.05 eV D) 13.6 eV

44. The radius of the nth Bohr orbit is given by r_n = a_0 * n^2 / Z, where a_0 is the Bohr radius. For hydrogen atom, Z=1. The radius of the 3rd orbit is:

A) a_0 B) 3a_0 C) 9a_0 D) a_0/3

45. The spectral lines of the Humphreys series correspond to transitions ending at which principal quantum number?

A) n = 4 B) n = 5 C) n = 6 D) n = 7

46. Which of the following statements about the hydrogen spectrum is incorrect?

A) Lyman series is in UV region. B) Balmer series is in visible region. C) Paschen series is in visible region. D) Brackett series is in IR region.

47. The energy difference between adjacent energy levels in a hydrogen atom decreases as:

A) n increases B) n decreases C) Z increases D) Z decreases

48. The Bohr radius (a_0) is approximately:

A) 5.3 x 10^-11 m B) 5.3 x 10^-10 m C) 5.3 x 10^-9 m D) 5.3 x 10^-12 m

49. The maximum number of photons emitted when an electron de-excites from n=4 to n=1 in a hydrogen atom is:

A) 3 B) 4 C) 5 D) 6

Energy levels and hydrogen spectrum - Online Test

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