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 orbital
B. ms II. Size of orbital
C. l III. Orientation of 
orbital
D. n IV. Orientation of spin
of 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 is located at \(\dfrac 5{36}\mathrm{ R_H~ cm^{-1}}\) (\(\mathrm{R_H}\) = Rydberg constant) 
Statement II:  When the temperature of blackbody increases, the maxima of the curve (intensity versus wavelength) shifts to 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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Given below are two statements: 
Statement I: The value of wave function, \(\Psi\) depends upon the coordinates of the electron in the atom. 
Statement II: The probability of finding an electron at a point within an atom is proportional to the orbital wave function. 
In light of the above statements, choose the correct answer from the options given below: 
   
1. Statement I is True but Statement II is False.
2. Statement I is False but Statement II is True.
3. Both Statement I and Statement II are True.
4. Both Statement I and Statement II are False.
Subtopic:  Quantum Numbers & Schrodinger Wave Equation |
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Identify the incorrect statement from the following:
1. The shapes of dxy, dyz, and dzx orbitals are similar to each other; and dx-y2 and dz2 are similar to each other.
2. All the five 5d orbitals are different in size when compared to the respective 4d orbitals.
3. All the five 4d orbitals have shapes similar to the respective 3d orbitals.
4. In an atom, all the five 3d orbitals are equal in energy in free state.
Subtopic:  Shell & Subshell |
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