A. If the ionisation energy of hydrogen atom is 13.6 eV then its ionisation potential is 13.6 V.
B. All the series of hydrogen spectrum have their respective shortest wavelength line corresponding to \( n = \infty \).
C. Paschen, Brackett and Pfund series all the three series are obtained in UV region.
D. The total energy of an electron is equal to the negative of its kinetic energy in the same orbit.
Choose the most appropriate answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A, B, D only
In the Bohr model of hydrogen the energy levels are \( E_n = -13.6/n^{2}\,\mathrm{eV} \), and each spectral series ends on one lower level.
(A) If the ionisation energy of hydrogen atom is 13.6 eV then its ionisation potential is 13.6 V. — Correct. The ionisation potential is the potential difference through which an electron must be accelerated to gain the ionisation energy; 13.6 eV of energy corresponds to 13.6 V.
(B) All the series of hydrogen spectrum have their respective shortest wavelength line corresponding to \( n = \infty \). — Correct. The largest energy gap, and so the shortest wavelength (the series limit), comes from a jump from \( n = \infty \) to the lower level of the series:
\( \displaystyle \frac{1}{\lambda} = R\left(\frac{1}{n_f^{2}} - \frac{1}{n_i^{2}}\right) \text{ is largest when } n_i = \infty \)
(C) Paschen, Brackett and Pfund series all the three series are obtained in UV region. — Incorrect. These three series end on \( n = 3, 4, 5 \); the energy gaps are small and the lines lie in the infrared region. Only the Lyman series lies in the ultraviolet.
(D) The total energy of an electron is equal to the negative of its kinetic energy in the same orbit. — Correct. For an orbit held by the Coulomb force, the potential energy is twice the kinetic energy with a negative sign:
\( U = -2K \)
\( E = K + U = -K \)