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Q. No.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
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 \(\left.\mathrm{R}_{\mathrm{H}}=2.18 \times 10^{-18} \mathrm{~J}, \mathrm{a}_0=52.9 \mathrm{pm}\right]\)
[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.
Choose the correct answer from the options given below:
| 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 |
| 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. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
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; and s=-\(\frac1{2}\)
II. \(n\)=3; \(l\)=2; \(m_l\)=1; and s=+\(\frac1{2}\)
III. \(n\)=4; \(l\)=1; \(m_l\)=0; and s=+\(\frac1{2}\)
IV. \(n\)=3; \(l\)=1; \(m_l\)=-1; and 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
I. \(n\)=4; \(l\)=2; \(m_l\)=-2; and s=-\(\frac1{2}\)
II. \(n\)=3; \(l\)=2; \(m_l\)=1; and s=+\(\frac1{2}\)
III. \(n\)=4; \(l\)=1; \(m_l\)=0; and s=+\(\frac1{2}\)
IV. \(n\)=3; \(l\)=1; \(m_l\)=-1; and 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:
In the light of the above statements, choose the correct answer from the options given below:
| 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. |
| 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. \(n_m = 2l^2 + 1 \)
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
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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