Modern Physics 1 Question 28
25. Consider the spectral line resulting from the transition $n=2 \rightarrow n=1$ in the atoms and ions given below. The shortest wavelength is produced by
(1983, 1M)
(a) hydrogen atom
(b) deuterium atom
(c) singly ionised helium
(d) doubly ionised lithium
Passage Based Questions
Passage 1
The key feature of Bohr’s theory of spectrum of hydrogen atom is the quantisation of angular momentum when an electron is revolving around a proton. We will extend this to a general rotational motion to find quantised rotational energy of a diatomic molecule assuming it to be rigid. The rule to be applied is Bohr’s quantisation condition.
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Solution:
- Shortest wavelength will correspond to maximum energy. As value of atomic number $(Z)$ increases, the magnitude of energy in different energy states gets increased. Value of $Z$ is maximum for doubly ionised lithium atom $(Z=3)$ among the given elements. Hence, wavelength corresponding to this will be least.
