307158
The energy of electron in first Bohr’s orbit of H-atom is –13.6 eV. What will be its potential energy in \({{\rm{4}}^{{\rm{th}}}}\) orbit ?
1 \({\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}\)
2 \({\rm{ - 3}}{\rm{.4}}\,{\rm{eV}}\)
3 \({\rm{ - 0}}{\rm{.85}}\,{\rm{eV}}\)
4 \({\rm{ - 1}}{\rm{.70}}\,{\rm{eV}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{n}}^{\rm{2}}}}}\) \({{\rm{E}}_{\rm{4}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{4}}^{\rm{2}}}}}{\rm{ = - 0}}{\rm{.85}}\,{\rm{eV}}\)
CHXI02:STRUCTURE OF ATOM
307160
If m and e are the mass and charge of the revolving electron in the orbit of radius r for hydrogen atom, the total energy of the revolving electron will be:
Total energy of a revolving electron is the sum of its kinetic and potential energy. Total energy \({\rm{ = K}}{\rm{.E + P}}{\rm{.E}}{\rm{.}}\) \({\rm{ = }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}{\rm{ + }}\left( {{\rm{ - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{\rm{r}}}} \right){\rm{ = - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}\)
JEE - 2014
CHXI02:STRUCTURE OF ATOM
307131
According to Bohr’s atomic theory, the correct statement is
1 Potential energy of electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
2 The product of velocity of electron and principal quantum number (n) \({\rm{\alpha }}\;{{\rm{Z}}^{\rm{2}}}\)
3 Frequency of revolution of electron in an orbit \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{3}}}}}\)
4 Coulombic force of attraction on the electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
Explanation:
\({\rm{v}} \propto \frac{{\rm{Z}}}{{\rm{n}}}{\rm{;r}} \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{\rm{Z}}}\) \(({\rm{1}}){\rm{P}}.{\rm{E}}. \propto \frac{{\rm{1}}}{{\rm{r}}} \propto \frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{2}}}}}\) \(({\rm{2}})\,{\rm{vn}} \propto {\rm{Z}}\) (3) Frequency of revolution \({\rm{ = }}\frac{{\rm{v}}}{{{\rm{2\pi }}{{\rm{r}}_{\rm{n}}}}}{\rm{ = }}\frac{{{\rm{Z/n}}}}{{{\rm{2\pi }}\left( {{{\rm{n}}^{\rm{2}}}{\rm{/Z}}} \right)}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{\rm{2\pi }}{{\rm{n}}^{\rm{3}}}}}\) Frequency \( \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{{{\rm{Z}}^{\rm{3}}}}}\) (4) Coulombic force of attraction \({\rm{ = }}\frac{{{\rm{Z}}{{\rm{e}}^{\rm{2}}}}}{{{\rm{(4\pi }}{{\rm{\varepsilon }}_{\rm{0}}}{\rm{)}}{{\rm{r}}^{\rm{2}}}}} \propto \frac{{\rm{Z}}}{{{{\rm{r}}^{\rm{2}}}}}{\rm{ = }}\frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{4}}}{\rm{/Z}}}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{4}}}}}\)
CHXI02:STRUCTURE OF ATOM
307132
The amount of energy required to remove the electron from a \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion in its ground state is how many times greater than the amount of energy needed to remove the electron from an H atom in its ground state?
1 \({\rm{2}}\)
2 \({\rm{9}}\)
3 \({\rm{4}}\)
4 \({\rm{6}}\)
Explanation:
For \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion and H atom in their ground state \({\rm{n = 1}}\). \(\frac{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{{\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}}}}}{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{\rm{H}}}}}{\rm{ = }}\frac{{{\rm{ - }}\frac{{{\rm{1312 \times (3}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{{\frac{{{\rm{1312 \times (1}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{\rm{ = 9}}\)
CHXI02:STRUCTURE OF ATOM
307133
The ionisation energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \({\rm{19}}{\rm{.6 \times 1}}{{\rm{0}}^{{\rm{ - 18}}}}{\rm{J}}\,{\rm{ato}}{{\rm{m}}^{{\rm{ - 1}}}}\) . The energy of the first stationary state of \({\rm{L}}{{\rm{i}}^{{\rm{ + 2}}}}\) will be
307158
The energy of electron in first Bohr’s orbit of H-atom is –13.6 eV. What will be its potential energy in \({{\rm{4}}^{{\rm{th}}}}\) orbit ?
1 \({\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}\)
2 \({\rm{ - 3}}{\rm{.4}}\,{\rm{eV}}\)
3 \({\rm{ - 0}}{\rm{.85}}\,{\rm{eV}}\)
4 \({\rm{ - 1}}{\rm{.70}}\,{\rm{eV}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{n}}^{\rm{2}}}}}\) \({{\rm{E}}_{\rm{4}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{4}}^{\rm{2}}}}}{\rm{ = - 0}}{\rm{.85}}\,{\rm{eV}}\)
CHXI02:STRUCTURE OF ATOM
307160
If m and e are the mass and charge of the revolving electron in the orbit of radius r for hydrogen atom, the total energy of the revolving electron will be:
Total energy of a revolving electron is the sum of its kinetic and potential energy. Total energy \({\rm{ = K}}{\rm{.E + P}}{\rm{.E}}{\rm{.}}\) \({\rm{ = }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}{\rm{ + }}\left( {{\rm{ - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{\rm{r}}}} \right){\rm{ = - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}\)
JEE - 2014
CHXI02:STRUCTURE OF ATOM
307131
According to Bohr’s atomic theory, the correct statement is
1 Potential energy of electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
2 The product of velocity of electron and principal quantum number (n) \({\rm{\alpha }}\;{{\rm{Z}}^{\rm{2}}}\)
3 Frequency of revolution of electron in an orbit \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{3}}}}}\)
4 Coulombic force of attraction on the electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
Explanation:
\({\rm{v}} \propto \frac{{\rm{Z}}}{{\rm{n}}}{\rm{;r}} \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{\rm{Z}}}\) \(({\rm{1}}){\rm{P}}.{\rm{E}}. \propto \frac{{\rm{1}}}{{\rm{r}}} \propto \frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{2}}}}}\) \(({\rm{2}})\,{\rm{vn}} \propto {\rm{Z}}\) (3) Frequency of revolution \({\rm{ = }}\frac{{\rm{v}}}{{{\rm{2\pi }}{{\rm{r}}_{\rm{n}}}}}{\rm{ = }}\frac{{{\rm{Z/n}}}}{{{\rm{2\pi }}\left( {{{\rm{n}}^{\rm{2}}}{\rm{/Z}}} \right)}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{\rm{2\pi }}{{\rm{n}}^{\rm{3}}}}}\) Frequency \( \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{{{\rm{Z}}^{\rm{3}}}}}\) (4) Coulombic force of attraction \({\rm{ = }}\frac{{{\rm{Z}}{{\rm{e}}^{\rm{2}}}}}{{{\rm{(4\pi }}{{\rm{\varepsilon }}_{\rm{0}}}{\rm{)}}{{\rm{r}}^{\rm{2}}}}} \propto \frac{{\rm{Z}}}{{{{\rm{r}}^{\rm{2}}}}}{\rm{ = }}\frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{4}}}{\rm{/Z}}}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{4}}}}}\)
CHXI02:STRUCTURE OF ATOM
307132
The amount of energy required to remove the electron from a \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion in its ground state is how many times greater than the amount of energy needed to remove the electron from an H atom in its ground state?
1 \({\rm{2}}\)
2 \({\rm{9}}\)
3 \({\rm{4}}\)
4 \({\rm{6}}\)
Explanation:
For \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion and H atom in their ground state \({\rm{n = 1}}\). \(\frac{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{{\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}}}}}{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{\rm{H}}}}}{\rm{ = }}\frac{{{\rm{ - }}\frac{{{\rm{1312 \times (3}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{{\frac{{{\rm{1312 \times (1}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{\rm{ = 9}}\)
CHXI02:STRUCTURE OF ATOM
307133
The ionisation energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \({\rm{19}}{\rm{.6 \times 1}}{{\rm{0}}^{{\rm{ - 18}}}}{\rm{J}}\,{\rm{ato}}{{\rm{m}}^{{\rm{ - 1}}}}\) . The energy of the first stationary state of \({\rm{L}}{{\rm{i}}^{{\rm{ + 2}}}}\) will be
307158
The energy of electron in first Bohr’s orbit of H-atom is –13.6 eV. What will be its potential energy in \({{\rm{4}}^{{\rm{th}}}}\) orbit ?
1 \({\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}\)
2 \({\rm{ - 3}}{\rm{.4}}\,{\rm{eV}}\)
3 \({\rm{ - 0}}{\rm{.85}}\,{\rm{eV}}\)
4 \({\rm{ - 1}}{\rm{.70}}\,{\rm{eV}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{n}}^{\rm{2}}}}}\) \({{\rm{E}}_{\rm{4}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{4}}^{\rm{2}}}}}{\rm{ = - 0}}{\rm{.85}}\,{\rm{eV}}\)
CHXI02:STRUCTURE OF ATOM
307160
If m and e are the mass and charge of the revolving electron in the orbit of radius r for hydrogen atom, the total energy of the revolving electron will be:
Total energy of a revolving electron is the sum of its kinetic and potential energy. Total energy \({\rm{ = K}}{\rm{.E + P}}{\rm{.E}}{\rm{.}}\) \({\rm{ = }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}{\rm{ + }}\left( {{\rm{ - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{\rm{r}}}} \right){\rm{ = - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}\)
JEE - 2014
CHXI02:STRUCTURE OF ATOM
307131
According to Bohr’s atomic theory, the correct statement is
1 Potential energy of electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
2 The product of velocity of electron and principal quantum number (n) \({\rm{\alpha }}\;{{\rm{Z}}^{\rm{2}}}\)
3 Frequency of revolution of electron in an orbit \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{3}}}}}\)
4 Coulombic force of attraction on the electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
Explanation:
\({\rm{v}} \propto \frac{{\rm{Z}}}{{\rm{n}}}{\rm{;r}} \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{\rm{Z}}}\) \(({\rm{1}}){\rm{P}}.{\rm{E}}. \propto \frac{{\rm{1}}}{{\rm{r}}} \propto \frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{2}}}}}\) \(({\rm{2}})\,{\rm{vn}} \propto {\rm{Z}}\) (3) Frequency of revolution \({\rm{ = }}\frac{{\rm{v}}}{{{\rm{2\pi }}{{\rm{r}}_{\rm{n}}}}}{\rm{ = }}\frac{{{\rm{Z/n}}}}{{{\rm{2\pi }}\left( {{{\rm{n}}^{\rm{2}}}{\rm{/Z}}} \right)}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{\rm{2\pi }}{{\rm{n}}^{\rm{3}}}}}\) Frequency \( \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{{{\rm{Z}}^{\rm{3}}}}}\) (4) Coulombic force of attraction \({\rm{ = }}\frac{{{\rm{Z}}{{\rm{e}}^{\rm{2}}}}}{{{\rm{(4\pi }}{{\rm{\varepsilon }}_{\rm{0}}}{\rm{)}}{{\rm{r}}^{\rm{2}}}}} \propto \frac{{\rm{Z}}}{{{{\rm{r}}^{\rm{2}}}}}{\rm{ = }}\frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{4}}}{\rm{/Z}}}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{4}}}}}\)
CHXI02:STRUCTURE OF ATOM
307132
The amount of energy required to remove the electron from a \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion in its ground state is how many times greater than the amount of energy needed to remove the electron from an H atom in its ground state?
1 \({\rm{2}}\)
2 \({\rm{9}}\)
3 \({\rm{4}}\)
4 \({\rm{6}}\)
Explanation:
For \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion and H atom in their ground state \({\rm{n = 1}}\). \(\frac{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{{\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}}}}}{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{\rm{H}}}}}{\rm{ = }}\frac{{{\rm{ - }}\frac{{{\rm{1312 \times (3}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{{\frac{{{\rm{1312 \times (1}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{\rm{ = 9}}\)
CHXI02:STRUCTURE OF ATOM
307133
The ionisation energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \({\rm{19}}{\rm{.6 \times 1}}{{\rm{0}}^{{\rm{ - 18}}}}{\rm{J}}\,{\rm{ato}}{{\rm{m}}^{{\rm{ - 1}}}}\) . The energy of the first stationary state of \({\rm{L}}{{\rm{i}}^{{\rm{ + 2}}}}\) will be
307158
The energy of electron in first Bohr’s orbit of H-atom is –13.6 eV. What will be its potential energy in \({{\rm{4}}^{{\rm{th}}}}\) orbit ?
1 \({\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}\)
2 \({\rm{ - 3}}{\rm{.4}}\,{\rm{eV}}\)
3 \({\rm{ - 0}}{\rm{.85}}\,{\rm{eV}}\)
4 \({\rm{ - 1}}{\rm{.70}}\,{\rm{eV}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{n}}^{\rm{2}}}}}\) \({{\rm{E}}_{\rm{4}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{4}}^{\rm{2}}}}}{\rm{ = - 0}}{\rm{.85}}\,{\rm{eV}}\)
CHXI02:STRUCTURE OF ATOM
307160
If m and e are the mass and charge of the revolving electron in the orbit of radius r for hydrogen atom, the total energy of the revolving electron will be:
Total energy of a revolving electron is the sum of its kinetic and potential energy. Total energy \({\rm{ = K}}{\rm{.E + P}}{\rm{.E}}{\rm{.}}\) \({\rm{ = }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}{\rm{ + }}\left( {{\rm{ - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{\rm{r}}}} \right){\rm{ = - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}\)
JEE - 2014
CHXI02:STRUCTURE OF ATOM
307131
According to Bohr’s atomic theory, the correct statement is
1 Potential energy of electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
2 The product of velocity of electron and principal quantum number (n) \({\rm{\alpha }}\;{{\rm{Z}}^{\rm{2}}}\)
3 Frequency of revolution of electron in an orbit \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{3}}}}}\)
4 Coulombic force of attraction on the electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
Explanation:
\({\rm{v}} \propto \frac{{\rm{Z}}}{{\rm{n}}}{\rm{;r}} \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{\rm{Z}}}\) \(({\rm{1}}){\rm{P}}.{\rm{E}}. \propto \frac{{\rm{1}}}{{\rm{r}}} \propto \frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{2}}}}}\) \(({\rm{2}})\,{\rm{vn}} \propto {\rm{Z}}\) (3) Frequency of revolution \({\rm{ = }}\frac{{\rm{v}}}{{{\rm{2\pi }}{{\rm{r}}_{\rm{n}}}}}{\rm{ = }}\frac{{{\rm{Z/n}}}}{{{\rm{2\pi }}\left( {{{\rm{n}}^{\rm{2}}}{\rm{/Z}}} \right)}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{\rm{2\pi }}{{\rm{n}}^{\rm{3}}}}}\) Frequency \( \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{{{\rm{Z}}^{\rm{3}}}}}\) (4) Coulombic force of attraction \({\rm{ = }}\frac{{{\rm{Z}}{{\rm{e}}^{\rm{2}}}}}{{{\rm{(4\pi }}{{\rm{\varepsilon }}_{\rm{0}}}{\rm{)}}{{\rm{r}}^{\rm{2}}}}} \propto \frac{{\rm{Z}}}{{{{\rm{r}}^{\rm{2}}}}}{\rm{ = }}\frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{4}}}{\rm{/Z}}}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{4}}}}}\)
CHXI02:STRUCTURE OF ATOM
307132
The amount of energy required to remove the electron from a \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion in its ground state is how many times greater than the amount of energy needed to remove the electron from an H atom in its ground state?
1 \({\rm{2}}\)
2 \({\rm{9}}\)
3 \({\rm{4}}\)
4 \({\rm{6}}\)
Explanation:
For \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion and H atom in their ground state \({\rm{n = 1}}\). \(\frac{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{{\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}}}}}{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{\rm{H}}}}}{\rm{ = }}\frac{{{\rm{ - }}\frac{{{\rm{1312 \times (3}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{{\frac{{{\rm{1312 \times (1}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{\rm{ = 9}}\)
CHXI02:STRUCTURE OF ATOM
307133
The ionisation energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \({\rm{19}}{\rm{.6 \times 1}}{{\rm{0}}^{{\rm{ - 18}}}}{\rm{J}}\,{\rm{ato}}{{\rm{m}}^{{\rm{ - 1}}}}\) . The energy of the first stationary state of \({\rm{L}}{{\rm{i}}^{{\rm{ + 2}}}}\) will be
307158
The energy of electron in first Bohr’s orbit of H-atom is –13.6 eV. What will be its potential energy in \({{\rm{4}}^{{\rm{th}}}}\) orbit ?
1 \({\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}\)
2 \({\rm{ - 3}}{\rm{.4}}\,{\rm{eV}}\)
3 \({\rm{ - 0}}{\rm{.85}}\,{\rm{eV}}\)
4 \({\rm{ - 1}}{\rm{.70}}\,{\rm{eV}}\)
Explanation:
\({{\rm{E}}_{\rm{n}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{n}}^{\rm{2}}}}}\) \({{\rm{E}}_{\rm{4}}}\) for \({\rm{H = }}\frac{{{\rm{ - 13}}{\rm{.6}}\,{\rm{eV}}}}{{{{\rm{4}}^{\rm{2}}}}}{\rm{ = - 0}}{\rm{.85}}\,{\rm{eV}}\)
CHXI02:STRUCTURE OF ATOM
307160
If m and e are the mass and charge of the revolving electron in the orbit of radius r for hydrogen atom, the total energy of the revolving electron will be:
Total energy of a revolving electron is the sum of its kinetic and potential energy. Total energy \({\rm{ = K}}{\rm{.E + P}}{\rm{.E}}{\rm{.}}\) \({\rm{ = }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}{\rm{ + }}\left( {{\rm{ - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{\rm{r}}}} \right){\rm{ = - }}\frac{{{{\rm{e}}^{\rm{2}}}}}{{{\rm{2r}}}}\)
JEE - 2014
CHXI02:STRUCTURE OF ATOM
307131
According to Bohr’s atomic theory, the correct statement is
1 Potential energy of electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
2 The product of velocity of electron and principal quantum number (n) \({\rm{\alpha }}\;{{\rm{Z}}^{\rm{2}}}\)
3 Frequency of revolution of electron in an orbit \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{3}}}}}\)
4 Coulombic force of attraction on the electron \({\rm{\alpha }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{2}}}}}\)
Explanation:
\({\rm{v}} \propto \frac{{\rm{Z}}}{{\rm{n}}}{\rm{;r}} \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{\rm{Z}}}\) \(({\rm{1}}){\rm{P}}.{\rm{E}}. \propto \frac{{\rm{1}}}{{\rm{r}}} \propto \frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{2}}}}}\) \(({\rm{2}})\,{\rm{vn}} \propto {\rm{Z}}\) (3) Frequency of revolution \({\rm{ = }}\frac{{\rm{v}}}{{{\rm{2\pi }}{{\rm{r}}_{\rm{n}}}}}{\rm{ = }}\frac{{{\rm{Z/n}}}}{{{\rm{2\pi }}\left( {{{\rm{n}}^{\rm{2}}}{\rm{/Z}}} \right)}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{\rm{2\pi }}{{\rm{n}}^{\rm{3}}}}}\) Frequency \( \propto \frac{{{{\rm{n}}^{\rm{2}}}}}{{{{\rm{Z}}^{\rm{3}}}}}\) (4) Coulombic force of attraction \({\rm{ = }}\frac{{{\rm{Z}}{{\rm{e}}^{\rm{2}}}}}{{{\rm{(4\pi }}{{\rm{\varepsilon }}_{\rm{0}}}{\rm{)}}{{\rm{r}}^{\rm{2}}}}} \propto \frac{{\rm{Z}}}{{{{\rm{r}}^{\rm{2}}}}}{\rm{ = }}\frac{{\rm{Z}}}{{{{\rm{n}}^{\rm{4}}}{\rm{/Z}}}}{\rm{ = }}\frac{{{{\rm{Z}}^{\rm{2}}}}}{{{{\rm{n}}^{\rm{4}}}}}\)
CHXI02:STRUCTURE OF ATOM
307132
The amount of energy required to remove the electron from a \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion in its ground state is how many times greater than the amount of energy needed to remove the electron from an H atom in its ground state?
1 \({\rm{2}}\)
2 \({\rm{9}}\)
3 \({\rm{4}}\)
4 \({\rm{6}}\)
Explanation:
For \({\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}\) ion and H atom in their ground state \({\rm{n = 1}}\). \(\frac{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{{\rm{L}}{{\rm{i}}^{{\rm{2 + }}}}}}}}{{{{{\rm{(}}{{\rm{E}}_{\rm{1}}}{\rm{)}}}_{\rm{H}}}}}{\rm{ = }}\frac{{{\rm{ - }}\frac{{{\rm{1312 \times (3}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{{\frac{{{\rm{1312 \times (1}}{{\rm{)}}^{\rm{2}}}}}{{{{{\rm{(1)}}}^{\rm{2}}}}}{\rm{kJ/mol}}}}{\rm{ = 9}}\)
CHXI02:STRUCTURE OF ATOM
307133
The ionisation energy of \({\rm{H}}{{\rm{e}}^{\rm{ + }}}\) is \({\rm{19}}{\rm{.6 \times 1}}{{\rm{0}}^{{\rm{ - 18}}}}{\rm{J}}\,{\rm{ato}}{{\rm{m}}^{{\rm{ - 1}}}}\) . The energy of the first stationary state of \({\rm{L}}{{\rm{i}}^{{\rm{ + 2}}}}\) will be
