The ratio of the wavelengths of the light absorbed by a Hydrogen atom when it undergoes \(n=2 \rightarrow n=3\) and \(n=4 \rightarrow n=6\) 
transitions, respectively, is
1. \(\dfrac{1}{9}\) 2. \(\dfrac{1}{4}\)
3. \(\dfrac{1}{36}\) 4. \(\dfrac{1}{16}\)
Subtopic:  Hydrogen Spectra |
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Energy and radius of the first Bohr orbit of \(He^+\) and \(Li^{2+}\) are 
[Given \(\left.\mathrm{R}_{\mathrm{H}}=2.18 \times 10^{-18} \mathrm{~J}, \mathrm{a}_0=52.9 \mathrm{pm}\right] \)
1. \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-19.62 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6\mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=8.72 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=26.4 \mathrm{pm} \end{aligned}\)
2. \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-8.72 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-19.62 \times 10^{-16} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=17.6 \mathrm{pm} \end{aligned}\)
3. \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=- 19.62 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=17.6 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-8.72 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=26.4 \mathrm{pm} \end{aligned}\)
4. \(\begin{aligned} & \mathrm{E}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=-8.72 \times 10^{-18} \mathrm{~J} \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{Li}^{2+}\right)=26.4 \mathrm{pm} \\ & \mathrm{E}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=-19.62 \times 10^{-18} \mathrm{~J} ; \\ & \mathrm{r}_{\mathrm{n}}\left(\mathrm{He}^{+}\right)=17.6 \mathrm{pm} \end{aligned} \)
Subtopic:  Bohr's Theory |
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The energy of electron in the ground state \((\text{n}=1)\) for \(\text{He}^+\) ion is \(\text{-x}J,\) then that for an electron in \(\text{n}=2\) state for \(\text{Be}^{3+}\) ion in \(\text{J}\) is :
1. \(-\dfrac x9\) 2. \(-4x\)
3. \(-\dfrac 49x\) 4. \(-x\)
Subtopic:  Bohr's Theory |
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Match List I with List II.
List I
Quantum Number
List II
Information provided
A. ml                                     I.         Shape of the orbital
B. ms II. Size of the orbital
C. l III. Orientation of the orbital
D. n IV. Orientation of spin of the electron
Choose the correct answer from the options given below:
1. A-III, B-IV, C-I, D-II 2. A-III, B-IV, C-II, D-I
3. A-II, B-I, C-IV, D-III 4. A-I, B-III, C-II, D-IV
Subtopic:  Quantum Numbers & Schrodinger Wave Equation |
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Isotope of an element contains \(19.23 \%\) more neutrons as compared to protons. The correct element along with its mass number is: (Given Atomic number \(\mathrm{Fe: 26, Co: 27}\) )
1. \(\mathrm {^{56}Fe }\) 2. \({ }^{57} \mathrm{Fe}\)
3. \({ }^{57} \mathrm{Co}\) 4. \({ }^{60} \mathrm{Co}\)
Subtopic:  Number of Electron, Proton & Neutron |
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Given below are two statement:
Statement I: The energy of the \(\mathrm{He}^{+}\) ion in \(n=2\) state is same as the energy of H atom in \(n=1\) state
Statement II: It is possible to determine simultaneously the exact position and exact momentum of an electron in \(\mathrm{H}\) atom.
In the light of the above Statements, choose the correct answer from the options given below:
1. Both Statement I and Statement II are True
2. Both Statement I and Statement II are False
3. Statement I is True but Statement II is False
4. Statement I is False but Statement II is True
Subtopic:  Bohr's Theory | Heisenberg Uncertainty Principle |
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The quantum numbers of four electrons are given below:
I. n=4; l=2; \(m_l\)=-2; s=-\(\frac1{2}\)
II. n=3; l=2; \(m_l\)=1; s=+\(\frac1{2}\)
III. n=4; l=1; \(m_l\)=0; s=+\(\frac1{2}\)
IV. n=3; l=1; \(m_l\)=-1; s=+\(\frac1{2}\)
The correct decreasing order of energy of these electrons is:

1. IV>II>III>I
2. I>III>II>IV
3. III>I>II>IV
4. I>II>III>IV
Subtopic:  Pauli's Exclusion Principle & Hund's Rule | AUFBAU Principle |

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Given below are two statements:
Statement I:  The Balmer spectral line for H atom with lowest energy  appears at \(\dfrac 5{36}\mathrm{ R_H~ cm^{-1}}\) (\(\mathrm{R_H}\) = Rydberg constant) 
Statement II:  When the temperature of a black body increases, the maxima of the curve (intensity versus wavelength) shifts towards shorter wavelength.
In the light of the above statements, choose the correct answer from the options given below:
 
1. Statement I is correct and Statement II is incorrect.
2. Statement I is incorrect and Statement II is correct.
3. Both Statement I and Statement II are correct.
4. Both Statement I and Statement II are incorrect.
Subtopic:  Bohr's Theory | Planck's Theory |
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The relation between \(n_m \) (\(n_m \) = number of permissible values of magnetic quantum number (ml) for a given value of azimuthal quantum number (l) is: 

1. \(n_m = l+2\)
2. \(l = {\dfrac{n_m -1} 2}\)
3. \(l= 2n_m +1\)
4. \(n_m = 2l^2 + 1 \)
Subtopic:  Shell & Subshell |
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Incorrect set of quantum numbers from the following is :

1. n=4,l=3, m1 =-3, -2, -1, 0, +1, +2, +3, ms=-1/2
2. n=5, l=2, m1 =-2, -1, +1, +2, ms=+1/2
3.  n=4, l=2, m1 = -2, -1, 0, +1, +2, ms=-1/2
4.  n=5,l=3, m1 =-3, -2, -1, 0, +1, +2, +3, ms=+1/2
Subtopic:  Quantum Numbers & Schrodinger Wave Equation |
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