307141
The ratio of the energy of electron in second excited state of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion to the electron in the first excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) is
1 \({\rm{81:16}}\)
2 \({\rm{9:16}}\)
3 \({\rm{16:81}}\)
4 \({\rm{16:9}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}{\rm{eV}}\) For \({{\rm{2}}^{{\rm{nd}}}}\) excited state of \({\rm{He}}_{}^{\rm{ + }}{\rm{,}}\,\;{\rm{n = 3}}\,{\rm{and}}\,{\rm{Z = 2}}\) \({{\rm{E}}_{\rm{3}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times (2}}{{\rm{)}}^{\rm{2}}}}}{{{{\rm{3}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 4}}}}{{\rm{9}}}{\rm{eV}}\) For \({1^{st}}\) excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}{\rm{,n = 2}}\) and \({\rm{Z = 3}}\) \({{\rm{E}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{3}}^{\rm{2}}}}}{{{{\rm{2}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 9}}}}{{\rm{4}}}{\rm{eV}}\) \(\frac{{{{\rm{E}}_{\rm{3}}}}}{{{{\rm{E}}_{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{4 \times 4}}}}{{{\rm{9 \times 9}}}}{\rm{ = }}\frac{{{\rm{16}}}}{{{\rm{81}}}}\)
CHXI02:STRUCTURE OF ATOM
307142
The energy of first stationary state \(({\rm{n}} = 1)\) of \({\rm{L}}{{\rm{i}}^{2 + }}\) if ionization energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \(19.6 \times {10^{ - 18}}{\rm{J}}\) \({\rm{ato}}{{\rm{m}}^{ - 1}}\) is
307141
The ratio of the energy of electron in second excited state of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion to the electron in the first excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) is
1 \({\rm{81:16}}\)
2 \({\rm{9:16}}\)
3 \({\rm{16:81}}\)
4 \({\rm{16:9}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}{\rm{eV}}\) For \({{\rm{2}}^{{\rm{nd}}}}\) excited state of \({\rm{He}}_{}^{\rm{ + }}{\rm{,}}\,\;{\rm{n = 3}}\,{\rm{and}}\,{\rm{Z = 2}}\) \({{\rm{E}}_{\rm{3}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times (2}}{{\rm{)}}^{\rm{2}}}}}{{{{\rm{3}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 4}}}}{{\rm{9}}}{\rm{eV}}\) For \({1^{st}}\) excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}{\rm{,n = 2}}\) and \({\rm{Z = 3}}\) \({{\rm{E}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{3}}^{\rm{2}}}}}{{{{\rm{2}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 9}}}}{{\rm{4}}}{\rm{eV}}\) \(\frac{{{{\rm{E}}_{\rm{3}}}}}{{{{\rm{E}}_{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{4 \times 4}}}}{{{\rm{9 \times 9}}}}{\rm{ = }}\frac{{{\rm{16}}}}{{{\rm{81}}}}\)
CHXI02:STRUCTURE OF ATOM
307142
The energy of first stationary state \(({\rm{n}} = 1)\) of \({\rm{L}}{{\rm{i}}^{2 + }}\) if ionization energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \(19.6 \times {10^{ - 18}}{\rm{J}}\) \({\rm{ato}}{{\rm{m}}^{ - 1}}\) is
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CHXI02:STRUCTURE OF ATOM
307141
The ratio of the energy of electron in second excited state of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion to the electron in the first excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) is
1 \({\rm{81:16}}\)
2 \({\rm{9:16}}\)
3 \({\rm{16:81}}\)
4 \({\rm{16:9}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}{\rm{eV}}\) For \({{\rm{2}}^{{\rm{nd}}}}\) excited state of \({\rm{He}}_{}^{\rm{ + }}{\rm{,}}\,\;{\rm{n = 3}}\,{\rm{and}}\,{\rm{Z = 2}}\) \({{\rm{E}}_{\rm{3}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times (2}}{{\rm{)}}^{\rm{2}}}}}{{{{\rm{3}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 4}}}}{{\rm{9}}}{\rm{eV}}\) For \({1^{st}}\) excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}{\rm{,n = 2}}\) and \({\rm{Z = 3}}\) \({{\rm{E}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{3}}^{\rm{2}}}}}{{{{\rm{2}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 9}}}}{{\rm{4}}}{\rm{eV}}\) \(\frac{{{{\rm{E}}_{\rm{3}}}}}{{{{\rm{E}}_{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{4 \times 4}}}}{{{\rm{9 \times 9}}}}{\rm{ = }}\frac{{{\rm{16}}}}{{{\rm{81}}}}\)
CHXI02:STRUCTURE OF ATOM
307142
The energy of first stationary state \(({\rm{n}} = 1)\) of \({\rm{L}}{{\rm{i}}^{2 + }}\) if ionization energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \(19.6 \times {10^{ - 18}}{\rm{J}}\) \({\rm{ato}}{{\rm{m}}^{ - 1}}\) is
307141
The ratio of the energy of electron in second excited state of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion to the electron in the first excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) is
1 \({\rm{81:16}}\)
2 \({\rm{9:16}}\)
3 \({\rm{16:81}}\)
4 \({\rm{16:9}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}{\rm{eV}}\) For \({{\rm{2}}^{{\rm{nd}}}}\) excited state of \({\rm{He}}_{}^{\rm{ + }}{\rm{,}}\,\;{\rm{n = 3}}\,{\rm{and}}\,{\rm{Z = 2}}\) \({{\rm{E}}_{\rm{3}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times (2}}{{\rm{)}}^{\rm{2}}}}}{{{{\rm{3}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 4}}}}{{\rm{9}}}{\rm{eV}}\) For \({1^{st}}\) excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}{\rm{,n = 2}}\) and \({\rm{Z = 3}}\) \({{\rm{E}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{3}}^{\rm{2}}}}}{{{{\rm{2}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 9}}}}{{\rm{4}}}{\rm{eV}}\) \(\frac{{{{\rm{E}}_{\rm{3}}}}}{{{{\rm{E}}_{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{4 \times 4}}}}{{{\rm{9 \times 9}}}}{\rm{ = }}\frac{{{\rm{16}}}}{{{\rm{81}}}}\)
CHXI02:STRUCTURE OF ATOM
307142
The energy of first stationary state \(({\rm{n}} = 1)\) of \({\rm{L}}{{\rm{i}}^{2 + }}\) if ionization energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \(19.6 \times {10^{ - 18}}{\rm{J}}\) \({\rm{ato}}{{\rm{m}}^{ - 1}}\) is
307141
The ratio of the energy of electron in second excited state of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) ion to the electron in the first excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) is
1 \({\rm{81:16}}\)
2 \({\rm{9:16}}\)
3 \({\rm{16:81}}\)
4 \({\rm{16:9}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}{\rm{eV}}\) For \({{\rm{2}}^{{\rm{nd}}}}\) excited state of \({\rm{He}}_{}^{\rm{ + }}{\rm{,}}\,\;{\rm{n = 3}}\,{\rm{and}}\,{\rm{Z = 2}}\) \({{\rm{E}}_{\rm{3}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times (2}}{{\rm{)}}^{\rm{2}}}}}{{{{\rm{3}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 4}}}}{{\rm{9}}}{\rm{eV}}\) For \({1^{st}}\) excited state of \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}{\rm{,n = 2}}\) and \({\rm{Z = 3}}\) \({{\rm{E}}_{\rm{2}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times }}{{\rm{3}}^{\rm{2}}}}}{{{{\rm{2}}^{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{ - 13}}{\rm{.6 \times 9}}}}{{\rm{4}}}{\rm{eV}}\) \(\frac{{{{\rm{E}}_{\rm{3}}}}}{{{{\rm{E}}_{\rm{2}}}}}{\rm{ = }}\frac{{{\rm{4 \times 4}}}}{{{\rm{9 \times 9}}}}{\rm{ = }}\frac{{{\rm{16}}}}{{{\rm{81}}}}\)
CHXI02:STRUCTURE OF ATOM
307142
The energy of first stationary state \(({\rm{n}} = 1)\) of \({\rm{L}}{{\rm{i}}^{2 + }}\) if ionization energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \(19.6 \times {10^{ - 18}}{\rm{J}}\) \({\rm{ato}}{{\rm{m}}^{ - 1}}\) is