Hydrogen Like Atom and its Line Spectra
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PHXII12:ATOMS

356513 One of the lines in the emission spectrum of \(L{i^{2 + }}\) has the same wavelength as that of the \({2^{nd{\rm{ }}}}\) line of Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is \(n = 12 \to n = x\). Find the value of \(x\).

1 8
2 6
3 7
4 5
PHXII12:ATOMS

356514 An electron in an excited state of \(L{i^{2 + }}\) ion has angular momentum \(\frac{{3h}}{{2\pi }}\). The de Broglie wavelength of electron in this state is \(P\pi {a_0}\) (where \({a_0}\) Bohr radius ). The value of \(P\) is

1 \(3\)
2 \(2\)
3 \(1\)
4 \(4\)
KCET - 2021
PHXII12:ATOMS

356515 Energy levels \(A,B\) and \(C\) of a certain atom correspond to increasing values of energy, i.e.,\({E_A} < {E_B} < {E_C}.\) If \({\lambda _1},{\lambda _2}\) and \({\lambda _3}\) are wavelength corresponding to transitions \(C\) to \(B,B\) to \(A\) and \(C\) to \(A\) respectively then
supporting img

1 \({\lambda _3} = \frac{{{\lambda _1}{\lambda _2}}}{{{\lambda _1} + {\lambda _2}}}\)
2 \({\lambda _3} = {\lambda _1} + {\lambda _2}\)
3 \(\lambda _3^2 = \lambda _1^2 + \lambda _2^2\)
4 \({\lambda _1} + {\lambda _2} + {\lambda _3}\)
PHXII12:ATOMS

356516 Using Bohr’s quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ( \(I = \) moment of inertia of diatomic molecule, \(h = \) Planck’s constant)

1 \(\frac{h}{{2I{\pi ^2}}}\)
2 \(\frac{{{h^2}}}{{2I{\pi ^2}}}\)
3 \(\frac{{{h^2}}}{{2{I^2}{\pi ^2}}}\)
4 \(\frac{h}{{2{I^2}\pi }}\)
MHTCET - 2020
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PHXII12:ATOMS

356513 One of the lines in the emission spectrum of \(L{i^{2 + }}\) has the same wavelength as that of the \({2^{nd{\rm{ }}}}\) line of Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is \(n = 12 \to n = x\). Find the value of \(x\).

1 8
2 6
3 7
4 5
PHXII12:ATOMS

356514 An electron in an excited state of \(L{i^{2 + }}\) ion has angular momentum \(\frac{{3h}}{{2\pi }}\). The de Broglie wavelength of electron in this state is \(P\pi {a_0}\) (where \({a_0}\) Bohr radius ). The value of \(P\) is

1 \(3\)
2 \(2\)
3 \(1\)
4 \(4\)
KCET - 2021
PHXII12:ATOMS

356515 Energy levels \(A,B\) and \(C\) of a certain atom correspond to increasing values of energy, i.e.,\({E_A} < {E_B} < {E_C}.\) If \({\lambda _1},{\lambda _2}\) and \({\lambda _3}\) are wavelength corresponding to transitions \(C\) to \(B,B\) to \(A\) and \(C\) to \(A\) respectively then
supporting img

1 \({\lambda _3} = \frac{{{\lambda _1}{\lambda _2}}}{{{\lambda _1} + {\lambda _2}}}\)
2 \({\lambda _3} = {\lambda _1} + {\lambda _2}\)
3 \(\lambda _3^2 = \lambda _1^2 + \lambda _2^2\)
4 \({\lambda _1} + {\lambda _2} + {\lambda _3}\)
PHXII12:ATOMS

356516 Using Bohr’s quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ( \(I = \) moment of inertia of diatomic molecule, \(h = \) Planck’s constant)

1 \(\frac{h}{{2I{\pi ^2}}}\)
2 \(\frac{{{h^2}}}{{2I{\pi ^2}}}\)
3 \(\frac{{{h^2}}}{{2{I^2}{\pi ^2}}}\)
4 \(\frac{h}{{2{I^2}\pi }}\)
MHTCET - 2020
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PHXII12:ATOMS

356513 One of the lines in the emission spectrum of \(L{i^{2 + }}\) has the same wavelength as that of the \({2^{nd{\rm{ }}}}\) line of Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is \(n = 12 \to n = x\). Find the value of \(x\).

1 8
2 6
3 7
4 5
PHXII12:ATOMS

356514 An electron in an excited state of \(L{i^{2 + }}\) ion has angular momentum \(\frac{{3h}}{{2\pi }}\). The de Broglie wavelength of electron in this state is \(P\pi {a_0}\) (where \({a_0}\) Bohr radius ). The value of \(P\) is

1 \(3\)
2 \(2\)
3 \(1\)
4 \(4\)
KCET - 2021
PHXII12:ATOMS

356515 Energy levels \(A,B\) and \(C\) of a certain atom correspond to increasing values of energy, i.e.,\({E_A} < {E_B} < {E_C}.\) If \({\lambda _1},{\lambda _2}\) and \({\lambda _3}\) are wavelength corresponding to transitions \(C\) to \(B,B\) to \(A\) and \(C\) to \(A\) respectively then
supporting img

1 \({\lambda _3} = \frac{{{\lambda _1}{\lambda _2}}}{{{\lambda _1} + {\lambda _2}}}\)
2 \({\lambda _3} = {\lambda _1} + {\lambda _2}\)
3 \(\lambda _3^2 = \lambda _1^2 + \lambda _2^2\)
4 \({\lambda _1} + {\lambda _2} + {\lambda _3}\)
PHXII12:ATOMS

356516 Using Bohr’s quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ( \(I = \) moment of inertia of diatomic molecule, \(h = \) Planck’s constant)

1 \(\frac{h}{{2I{\pi ^2}}}\)
2 \(\frac{{{h^2}}}{{2I{\pi ^2}}}\)
3 \(\frac{{{h^2}}}{{2{I^2}{\pi ^2}}}\)
4 \(\frac{h}{{2{I^2}\pi }}\)
MHTCET - 2020
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PHXII12:ATOMS

356513 One of the lines in the emission spectrum of \(L{i^{2 + }}\) has the same wavelength as that of the \({2^{nd{\rm{ }}}}\) line of Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is \(n = 12 \to n = x\). Find the value of \(x\).

1 8
2 6
3 7
4 5
PHXII12:ATOMS

356514 An electron in an excited state of \(L{i^{2 + }}\) ion has angular momentum \(\frac{{3h}}{{2\pi }}\). The de Broglie wavelength of electron in this state is \(P\pi {a_0}\) (where \({a_0}\) Bohr radius ). The value of \(P\) is

1 \(3\)
2 \(2\)
3 \(1\)
4 \(4\)
KCET - 2021
PHXII12:ATOMS

356515 Energy levels \(A,B\) and \(C\) of a certain atom correspond to increasing values of energy, i.e.,\({E_A} < {E_B} < {E_C}.\) If \({\lambda _1},{\lambda _2}\) and \({\lambda _3}\) are wavelength corresponding to transitions \(C\) to \(B,B\) to \(A\) and \(C\) to \(A\) respectively then
supporting img

1 \({\lambda _3} = \frac{{{\lambda _1}{\lambda _2}}}{{{\lambda _1} + {\lambda _2}}}\)
2 \({\lambda _3} = {\lambda _1} + {\lambda _2}\)
3 \(\lambda _3^2 = \lambda _1^2 + \lambda _2^2\)
4 \({\lambda _1} + {\lambda _2} + {\lambda _3}\)
PHXII12:ATOMS

356516 Using Bohr’s quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ( \(I = \) moment of inertia of diatomic molecule, \(h = \) Planck’s constant)

1 \(\frac{h}{{2I{\pi ^2}}}\)
2 \(\frac{{{h^2}}}{{2I{\pi ^2}}}\)
3 \(\frac{{{h^2}}}{{2{I^2}{\pi ^2}}}\)
4 \(\frac{h}{{2{I^2}\pi }}\)
MHTCET - 2020