A particle of mass \(m\) is moving around the origin with a constant force \(F\) pulling it towards the origin. If Bohr model is used to describe its motion, the radius \(r\) of the \(n^{\text{th}}\) orbit and the particle's speed \(v\) in the orbit depend on \(n\) as:
1. \(r \propto n^{2/3}; v \propto n^{1/3}\)
2. \(r \propto n^{4/3}; v \propto n^{-1/3}\)
3. \(r \propto n^{1/3}; v \propto n^{1/3}\)
4. \(r \propto n^{1/3}; v \propto n^{2/3}\)
Subtopic:  Bohr's Model of Atom |
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Match List I with List II.
List I
(Spectral Lines of Hydrogen for transitions from)
List II
(Wavelength (nm))
\(\mathrm{A.}\) \(n_2=3\)  to \(n_1=2\)  \(\mathrm{I.}\) \(410.2\)
\(\mathrm{B.}\) \(n_2=4\)  to \(n_1=2\)  \(\mathrm{II.}\) \(434.1\)
\(\mathrm{C.}\) \(n_2=5\)  to \(n_1=2\)  \(\mathrm{III.}\) \(656.3\)
\(\mathrm{D.}\) \(n_2=6\) to \(n_1=2\)  \(\mathrm{IV.}\) \(486.1\)
 
Choose the correct answer from the options given below:
1. \(\mathrm{A - III, B - IV, C - II, D - I}\)
2. \(\mathrm{A - IV, B - III, C - I, D - II}\)
3. \(\mathrm{A - I, B - II, C - III, D - IV}\)
4. \(\mathrm{A - II, B - I, C - IV, D - III}\)
Subtopic:  Spectral Series |
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Given below are two statements:
Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges.
Statement II: Atoms of each element are stable and emit their characteristic spectrum.
 
In the light of the above statements, choose the most appropriate answer from the options given below:
1. Both Statement I and Statement II are incorrect.
2. Statement I is correct but Statement II is incorrect.
3. Statement I is incorrect but Statement II is correct.
4. Both Statement I and Statement II are correct.
Subtopic:  Spectral Series |
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Match List-I (Spectral Series) with List-II (corresponding wave number expressions).
List-I
(Series)
List-II
(Wave number in \(\text{cm}^{–1}\))
A. Balmer series I. \( R\left(\dfrac{1}{1^2}-\dfrac{1}{n^2}\right) \)
B. Lyman series II. \( R\left(\dfrac{1}{4^2}-\dfrac{1}{n^2}\right) \)
C. Brackett series III. \( R\left(\dfrac{1}{5^2}-\dfrac{1}{n^2}\right) \)
D. Pfund series  IV. \( R\left(\dfrac{1}{2^2}-\dfrac{1}{n^2}\right)\)
Choose the correct answer from the options given below:
1. A-I, B-IV, C-III, D-II
2. A-II, B-III, C-IV, D-I
3. A-IV, B-I, C-II, D-III
4. A-III, B-II, C-I, D-IV
Subtopic:  Spectral Series |
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The spectral series which corresponds to the electronic transition from the levels \({n}_{2}=5,6,\ldots \) to the level \({n}_{1}=4\mathrm~\) is:
1. Pfund series 2. Brackett series
3. Lyman series 4. Balmer series
Subtopic:  Spectral Series |
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Some energy levels of a molecule are shown in the figure with their wavelengths of transitions.
Then:
1. \(\lambda_{3}>\lambda_{2},\lambda_{1}=2\lambda_{2}\) 2. \(\lambda_{3}>\lambda_{2},\lambda_{1}=4\lambda_{2}\)
3. \(\lambda_{1}>\lambda_{2},\lambda_{2}=2\lambda_{3}\) 4. \(\lambda_{2}>\lambda_{1},\lambda_{2}=2\lambda_{3}\)
Subtopic:  Spectral Series |
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In hydrogen spectrum, the shortest wavelength in the Balmer series is \(\lambda\). The shortest wavelength in the Bracket series is:
1. \(16\lambda\)
2. \(2\lambda\)
3. \(4\lambda\)
4. \(9\lambda\)
Subtopic:  Spectral Series |
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The radius of innermost orbit of a hydrogen atom is \(5.3 \times 10^{-11}~\text m.\) What is the radius of the third allowed orbit of a hydrogen atom?
1. \(4.77~ \mathring{A}\)
2. \(0.53~ \mathring{A}\)
3. \(1.06~ \mathring{A}\)
4. \(1.59~ \mathring{A}\)
Subtopic:  Bohr's Model of Atom |
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The ground state energy of a hydrogen atom is \(-13.6~\text{eV}.\) The energy needed to ionize the hydrogen atom from its second excited state will be:
1. \(13.6~\text{eV}\)
2. \(6.8~\text{eV}\)
3. \(1.51~\text{eV}\)
4. \(3.4~\text{eV}\)
Subtopic:  Bohr's Model of Atom |
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The wavelength of the Lyman series of hydrogen atom appears in:
1. visible region
2. far infrared region
3. ultraviolet region
4. infrared region
Subtopic:  Spectral Series |
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