Three statements are made about emission and absorption spectra.
I. They provide information on the chemical composition of substances.
II. They provide evidence for mass-energy equivalence.
III. They arise from transitioning electrons between energy levels.
Which of the statements are correct?
Correct Answer: \( \boxed{\mathrm{B}} \)
Emission and absorption spectra consist of characteristic wavelengths associated with transitions between quantised electron energy levels.
When an electron changes between energy levels, the energy difference is related to the photon frequency by
\(\Delta E=hf\)
Different elements have different sets of energy levels, producing characteristic spectra. Therefore, spectra can be used to identify the chemical composition of substances.
Hence, statement I is correct.
The spectra arise from electrons transitioning between discrete energy levels, so statement III is also correct.
Mass-energy equivalence refers to the relationship
\(E=mc^2\)
Emission and absorption spectra provide evidence for quantised energy levels, not mass-energy equivalence. Therefore, statement II is incorrect.
Hence, the correct answer is \( \boxed{\mathrm{B}} \).
For which of the following atoms would the Bohr model apply, if one electron was removed from the atom?
Correct Answer: \( \boxed{\mathrm{D}} \)
The Bohr model is applicable to hydrogen-like atoms or ions, which contain only one electron.
A neutral helium atom, \(^{4}_{2}\mathrm{He}\), contains two electrons.
If one electron is removed, the resulting helium ion has only one electron:
\(\mathrm{He}^{+}\)
This is a hydrogen-like ion, so the Bohr model can be applied.
For comparison, removing one electron from sodium leaves \(10\) electrons, removing one from lithium leaves \(2\) electrons, and removing one from uranium leaves many electrons. These are not one-electron systems.
Hence, the correct answer is \( \boxed{\mathrm{D}} \).
In the Bohr model for hydrogen:
\( r_n \propto n^2 \) and \( v_n \propto \dfrac{1}{n} \).
The question states that \( r_{2} = 4 r_{1} \), which is consistent with \( r_n \propto n^2 \).
Since \( v_n \propto \dfrac{1}{n} \), the ratio of speeds is
\[ \frac{v_{2}}{v_{1}} = \frac{1/2}{1/1} = \frac{1}{2}. \]
✅ Answer: (B)
