Energy Levels and Spectral Series - UNSOLVED PRACTICE SET

Q7. Draw an energy level diagram for the hydrogen atom showing the first four energy levels.

Q8. What is the significance of the negative sign in the energy expression E_n = −13.6/n² eV?

Q9. Name the different spectral series of hydrogen and the region of the electromagnetic spectrum in which each lies.

Q10. Calculate the wavelength of the first line of the Balmer series.

Q11. What is the maximum number of spectral lines emitted when an electron in a hydrogen atom makes a transition from the n = 4 level to the ground state?

Q12. Why does the hydrogen spectrum consist of discrete lines rather than a continuous spectrum?

Q13. Derive the expression for the energy of the electron in the nth orbit of a hydrogen atom. Draw the energy level diagram and explain how spectral lines are produced.

Q14. State and explain the Rydberg formula. Show how it can be used to calculate the wavelengths of spectral lines in different series of the hydrogen spectrum.

Q15. Explain the origin of the Lyman, Balmer, and Paschen series in the hydrogen spectrum. Draw the energy level diagram showing the transitions responsible for these series.

Q16. For a hydrogen atom:

(a) Calculate the energy required to ionize the atom from its ground state.

(b) Calculate the wavelength of the photon required for this ionization.

(c) Calculate the wavelength of the first line of the Lyman series.

(d) Calculate the wavelength of the series limit of the Balmer series.

Q17. An electron in a hydrogen atom makes a transition from an excited state to the ground state and emits a photon of wavelength 102.6 nm.

(a) Identify the initial energy level of the electron.

(b) Calculate the energy of the emitted photon in eV.

(c) If the atom is initially in the n = 5 state, calculate the number of different spectral lines that can be emitted as the electron returns to the ground state.

Q18. In your school's physics lab, a student is studying the hydrogen spectrum using a discharge tube.

(a) She observes a red line in the spectrum and measures its wavelength as 656 nm. Identify which transition in the hydrogen atom produces this line and calculate the energy difference involved.

(b) The student then calculates the wavelength of the second line of the Balmer series (transition from n = 4 to n = 2). Verify that it is approximately 486 nm.

(c) A classmate asks why the hydrogen spectrum in the discharge tube shows only certain colours and not a continuous rainbow. Explain using the concept of energy levels and quantized transitions.

(d) The student learns that the Sun's spectrum contains dark lines (Fraunhofer lines) at the same wavelengths as hydrogen's emission lines. Explain how absorption spectra are formed and why they appear as dark lines.

(e) In astrophysics, the redshift of spectral lines tells us that distant galaxies are moving away from us. If a hydrogen line normally at 656 nm is observed at 660 nm from a distant galaxy, calculate the speed of recession of the galaxy.