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The orbital angular momentum for an electron revolving in an orbit is given by $ \sqrt { l ( l+1 )} . { h \over 2 \pi } $ This momentum for an s-electron will be given by

A. $ + { 1 \over2 } { h \over 2 \pi } $ B. zero C. $ { h \over 2 \pi } $ D. $ \sqrt 2 { h \over 2 \pi } $

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Explanation

The orbital angular momentum for an electron is given by âˆš[l(l+1)] Ä§/2Ï€, where l is the orbital angular momentum quantum number. For an s-electron, l=0, so âˆš[l(l+1)] becomes 0, and the orbital angular momentum is zero.

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The emission spectrum of hydrogen is found to satisfy the expression for the energy change â€œE (in Joules) such that $ â€œE = 2Â·18 \times 10^{â€“18} J where n_1 = 1,2, 3 ..........and n_2 = 2,3 ,4 $ The spectral lines correspond to Paschen series it

A. $ n_1 = 1 and n_2 = 2, 3, 4 $ B. $ n_1 = 3 and n_2 = 4, 5, 6 $ C. $ n_1 = 1 and n_2 = 3, 4, 5 $ D. $ n_1 = 2 and n_2 = 3, 4, 5 $

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Among the following series of transition metal ions, the one where all metal ions have same 3d electronic configuration is

A. $ Ti^{2+} , V^{3+}, Cr ^ {4+} , Mn ^ {5+} $ B. $ Ti^{2+} , V^{2+}, Cr ^ {3+} , Mn ^ {4+} $ C. $ Ti^{+} , V^{4+}, Cr ^ {6+} , Mn ^ {7+} $ D. $ Ti^{4+} , V^{3+}, Cr ^ {2+} , Mn ^ {3+} $

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For d-electron, the orbital angular momentum is

$ \sqrt { 6 } h / 2 \pi $

$ \sqrt { 2h / 2 \pi } $

$ h / 2 \pi $

$ 2h / \pi $

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Explanation

Where the value of l for d orbital is 2

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Time taken for an electron to complete one revolution in the Bohr orbit of hydrogen atom is

A. $ { 4 \pi ^2 m r ^2 \over nh } $ B. $ { nh \over 4 \pi ^2 mr } $ C. $ {2 \pi mr \over n ^2 h ^2 } $ D. $ { h \over 2 \pi mr }$

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Which of the following sets of quantum numbers is correct for an electron in 4f – orbital ?

n = 4, l= 3, m = +4, s = + 1 /2

n = 3, l= 2, m = -2, s = + 1 /2

n = 4,l = 3, m = +1, s = + 1 /2

n = 4, l= 4, m = -4, s = - 1 /2

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Explanation

The correct set of quantum numbers for an electron in the 4f orbital is n = 4, l = 3 (for f orbital), m = +1, s = +1/2. The principal quantum number (n) determines the shell, l determines the subshell, m determines the orientation, and s represents the spin of the electron.

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The wavelength of radiation emitted when in a hydrogen atom electron falls from infinity to stationary state 1, would be (Rydberg constant ï€½ 1·09 × 107m–1)

91nm

$ 9·1 \times 10^{–8} nm $

406 nm

192 nm

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Explanation

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The relationship between energy E, of the radiation with a wavelength 8000 Ã… and the energy of the radiation with a wavelength 16000 Ã… is

A. $ E_1 = 6 E_2 $ B. $ E_1 = 2 E_2 $ C. $ E_1 = 4 E_2 $ D. $ E_1 = 1/2 E_2 $

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The energy of second Bohr orbit of the hydrogen atom is $ â€“328 kJ mol^{â€“1} $ , hence the energy of fourth Bohr orbit would be

A. $ â€“41 kJ mol^{â€“1} $ B. $ â€“1312 kJ mol^{â€“1} $ C. $ â€“164 kJ mol^{â€“1} $ D. $ â€“82 kJ mol^{â€“1} $

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Explanation

The energy of an electron in the Bohr model of the hydrogen atom is given by E = -13.6/n^2 eV, where n is the principal quantum number. For n = 2, E = -13.6/2^2 = -3.4 eV or -328 kJ/mol. For n = 4, E = -13.6/4^2 = -0.85 eV or -82 kJ/mol.

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Which of the following statements in relation to the hydrogen atom is correct?

A. 3s-orbital is lower in energy than 3p-orbital B. 3p-orbital is lower in energy than 3d-orbital C. 3s and 3p orbitals arc of lower energy than 3d orbital D. 3s, 3p and 3d orbitals all have the same energy.

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