356472
The electron of a hydrogen atom revolves around the proton in a circular nth orbit of radius \({r_n} = {\varepsilon _0}{n^2}{h^2}/(\pi m{e^2})\) with speed,\({v_n} = \frac{{{e^2}}}{{2{\varepsilon _0}nh}}\) . The current due to the circulating charge is proportional to
1 \({e^2}\)
2 \({e^3}\)
3 \({e^5}\)
4 \({e^6}\)
Explanation:
Time period of electron, \(T = \frac{{2\pi r}}{v} = \frac{{\frac{{2\pi \times {\varepsilon _0}{n^2}{h^2}}}{{\pi m{e^2}}}}}{{\frac{{{e^2}}}{{2{\varepsilon _0}nh}}}} = \frac{{4\varepsilon _0^2{n^3}{h^3}}}{{m{e^4}}}\) Now currrent, \(i = \frac{e}{T} = \frac{e}{{4\varepsilon _0^2{n^3}{h^3}/m{e^4}}} = \frac{{m{e^5}}}{{4\varepsilon _0^2{n^3}{h^3}}} \Rightarrow i\,\,\alpha \,\,{e^5}\)
PHXII12:ATOMS
356473
The ratio of area of first excited state to ground state of orbit of hydrogen atom is
1 \({1: 16}\)
2 \({1: 4}\)
3 \({4: 1}\)
4 \({16: 1}\)
Explanation:
Radius of electron orbit is related with the orbit number as \({r \propto n^{2}}\). \({\therefore}\) Area \({\propto r^{2} \propto n^{4}}\) \({\dfrac{A_{1}}{A_{2}}=\left(\dfrac{n_{1}}{n_{2}}\right)^{4}=\left(\dfrac{2}{1}\right)=\dfrac{16}{1}}\)
KCET - 2024
PHXII12:ATOMS
356474
Statement A : Electrons in the atom are held due to coulomb forces. Statement B : The atom is stable only because the centripetal force due to Coulomb’s law is balanced by the centrifugal force
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
According to postulates of Bohr’s atom model the electron revolves around the nucleus in fixed orbit of definite radii. As long as the electron is in a certain orbit it does not radiate any energy.
PHXII12:ATOMS
356475
The value of ground state energy of a \(H\)-atom is \( - 13.6\,eV\). The energy required to take an electron from ground state to the first excited state is:
Speed of the electron in Bohr’s \(n{\rm{th}}\) orbit is \(v = \frac{{Z{e^2}}}{{2{\varepsilon _0}nh}}\) For \(n = 1,\) \({v_1} = 2.19 \times {10^6}m/s\) For \(n = 2,{v_2} = 1.095 \times {10^6}m/s\) For \(n = 3,{v_3} = 7.3 \times {10^5}m/s\)
356472
The electron of a hydrogen atom revolves around the proton in a circular nth orbit of radius \({r_n} = {\varepsilon _0}{n^2}{h^2}/(\pi m{e^2})\) with speed,\({v_n} = \frac{{{e^2}}}{{2{\varepsilon _0}nh}}\) . The current due to the circulating charge is proportional to
1 \({e^2}\)
2 \({e^3}\)
3 \({e^5}\)
4 \({e^6}\)
Explanation:
Time period of electron, \(T = \frac{{2\pi r}}{v} = \frac{{\frac{{2\pi \times {\varepsilon _0}{n^2}{h^2}}}{{\pi m{e^2}}}}}{{\frac{{{e^2}}}{{2{\varepsilon _0}nh}}}} = \frac{{4\varepsilon _0^2{n^3}{h^3}}}{{m{e^4}}}\) Now currrent, \(i = \frac{e}{T} = \frac{e}{{4\varepsilon _0^2{n^3}{h^3}/m{e^4}}} = \frac{{m{e^5}}}{{4\varepsilon _0^2{n^3}{h^3}}} \Rightarrow i\,\,\alpha \,\,{e^5}\)
PHXII12:ATOMS
356473
The ratio of area of first excited state to ground state of orbit of hydrogen atom is
1 \({1: 16}\)
2 \({1: 4}\)
3 \({4: 1}\)
4 \({16: 1}\)
Explanation:
Radius of electron orbit is related with the orbit number as \({r \propto n^{2}}\). \({\therefore}\) Area \({\propto r^{2} \propto n^{4}}\) \({\dfrac{A_{1}}{A_{2}}=\left(\dfrac{n_{1}}{n_{2}}\right)^{4}=\left(\dfrac{2}{1}\right)=\dfrac{16}{1}}\)
KCET - 2024
PHXII12:ATOMS
356474
Statement A : Electrons in the atom are held due to coulomb forces. Statement B : The atom is stable only because the centripetal force due to Coulomb’s law is balanced by the centrifugal force
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
According to postulates of Bohr’s atom model the electron revolves around the nucleus in fixed orbit of definite radii. As long as the electron is in a certain orbit it does not radiate any energy.
PHXII12:ATOMS
356475
The value of ground state energy of a \(H\)-atom is \( - 13.6\,eV\). The energy required to take an electron from ground state to the first excited state is:
Speed of the electron in Bohr’s \(n{\rm{th}}\) orbit is \(v = \frac{{Z{e^2}}}{{2{\varepsilon _0}nh}}\) For \(n = 1,\) \({v_1} = 2.19 \times {10^6}m/s\) For \(n = 2,{v_2} = 1.095 \times {10^6}m/s\) For \(n = 3,{v_3} = 7.3 \times {10^5}m/s\)
356472
The electron of a hydrogen atom revolves around the proton in a circular nth orbit of radius \({r_n} = {\varepsilon _0}{n^2}{h^2}/(\pi m{e^2})\) with speed,\({v_n} = \frac{{{e^2}}}{{2{\varepsilon _0}nh}}\) . The current due to the circulating charge is proportional to
1 \({e^2}\)
2 \({e^3}\)
3 \({e^5}\)
4 \({e^6}\)
Explanation:
Time period of electron, \(T = \frac{{2\pi r}}{v} = \frac{{\frac{{2\pi \times {\varepsilon _0}{n^2}{h^2}}}{{\pi m{e^2}}}}}{{\frac{{{e^2}}}{{2{\varepsilon _0}nh}}}} = \frac{{4\varepsilon _0^2{n^3}{h^3}}}{{m{e^4}}}\) Now currrent, \(i = \frac{e}{T} = \frac{e}{{4\varepsilon _0^2{n^3}{h^3}/m{e^4}}} = \frac{{m{e^5}}}{{4\varepsilon _0^2{n^3}{h^3}}} \Rightarrow i\,\,\alpha \,\,{e^5}\)
PHXII12:ATOMS
356473
The ratio of area of first excited state to ground state of orbit of hydrogen atom is
1 \({1: 16}\)
2 \({1: 4}\)
3 \({4: 1}\)
4 \({16: 1}\)
Explanation:
Radius of electron orbit is related with the orbit number as \({r \propto n^{2}}\). \({\therefore}\) Area \({\propto r^{2} \propto n^{4}}\) \({\dfrac{A_{1}}{A_{2}}=\left(\dfrac{n_{1}}{n_{2}}\right)^{4}=\left(\dfrac{2}{1}\right)=\dfrac{16}{1}}\)
KCET - 2024
PHXII12:ATOMS
356474
Statement A : Electrons in the atom are held due to coulomb forces. Statement B : The atom is stable only because the centripetal force due to Coulomb’s law is balanced by the centrifugal force
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
According to postulates of Bohr’s atom model the electron revolves around the nucleus in fixed orbit of definite radii. As long as the electron is in a certain orbit it does not radiate any energy.
PHXII12:ATOMS
356475
The value of ground state energy of a \(H\)-atom is \( - 13.6\,eV\). The energy required to take an electron from ground state to the first excited state is:
Speed of the electron in Bohr’s \(n{\rm{th}}\) orbit is \(v = \frac{{Z{e^2}}}{{2{\varepsilon _0}nh}}\) For \(n = 1,\) \({v_1} = 2.19 \times {10^6}m/s\) For \(n = 2,{v_2} = 1.095 \times {10^6}m/s\) For \(n = 3,{v_3} = 7.3 \times {10^5}m/s\)
NEET Test Series from KOTA - 10 Papers In MS WORD
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PHXII12:ATOMS
356472
The electron of a hydrogen atom revolves around the proton in a circular nth orbit of radius \({r_n} = {\varepsilon _0}{n^2}{h^2}/(\pi m{e^2})\) with speed,\({v_n} = \frac{{{e^2}}}{{2{\varepsilon _0}nh}}\) . The current due to the circulating charge is proportional to
1 \({e^2}\)
2 \({e^3}\)
3 \({e^5}\)
4 \({e^6}\)
Explanation:
Time period of electron, \(T = \frac{{2\pi r}}{v} = \frac{{\frac{{2\pi \times {\varepsilon _0}{n^2}{h^2}}}{{\pi m{e^2}}}}}{{\frac{{{e^2}}}{{2{\varepsilon _0}nh}}}} = \frac{{4\varepsilon _0^2{n^3}{h^3}}}{{m{e^4}}}\) Now currrent, \(i = \frac{e}{T} = \frac{e}{{4\varepsilon _0^2{n^3}{h^3}/m{e^4}}} = \frac{{m{e^5}}}{{4\varepsilon _0^2{n^3}{h^3}}} \Rightarrow i\,\,\alpha \,\,{e^5}\)
PHXII12:ATOMS
356473
The ratio of area of first excited state to ground state of orbit of hydrogen atom is
1 \({1: 16}\)
2 \({1: 4}\)
3 \({4: 1}\)
4 \({16: 1}\)
Explanation:
Radius of electron orbit is related with the orbit number as \({r \propto n^{2}}\). \({\therefore}\) Area \({\propto r^{2} \propto n^{4}}\) \({\dfrac{A_{1}}{A_{2}}=\left(\dfrac{n_{1}}{n_{2}}\right)^{4}=\left(\dfrac{2}{1}\right)=\dfrac{16}{1}}\)
KCET - 2024
PHXII12:ATOMS
356474
Statement A : Electrons in the atom are held due to coulomb forces. Statement B : The atom is stable only because the centripetal force due to Coulomb’s law is balanced by the centrifugal force
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
According to postulates of Bohr’s atom model the electron revolves around the nucleus in fixed orbit of definite radii. As long as the electron is in a certain orbit it does not radiate any energy.
PHXII12:ATOMS
356475
The value of ground state energy of a \(H\)-atom is \( - 13.6\,eV\). The energy required to take an electron from ground state to the first excited state is:
Speed of the electron in Bohr’s \(n{\rm{th}}\) orbit is \(v = \frac{{Z{e^2}}}{{2{\varepsilon _0}nh}}\) For \(n = 1,\) \({v_1} = 2.19 \times {10^6}m/s\) For \(n = 2,{v_2} = 1.095 \times {10^6}m/s\) For \(n = 3,{v_3} = 7.3 \times {10^5}m/s\)
356472
The electron of a hydrogen atom revolves around the proton in a circular nth orbit of radius \({r_n} = {\varepsilon _0}{n^2}{h^2}/(\pi m{e^2})\) with speed,\({v_n} = \frac{{{e^2}}}{{2{\varepsilon _0}nh}}\) . The current due to the circulating charge is proportional to
1 \({e^2}\)
2 \({e^3}\)
3 \({e^5}\)
4 \({e^6}\)
Explanation:
Time period of electron, \(T = \frac{{2\pi r}}{v} = \frac{{\frac{{2\pi \times {\varepsilon _0}{n^2}{h^2}}}{{\pi m{e^2}}}}}{{\frac{{{e^2}}}{{2{\varepsilon _0}nh}}}} = \frac{{4\varepsilon _0^2{n^3}{h^3}}}{{m{e^4}}}\) Now currrent, \(i = \frac{e}{T} = \frac{e}{{4\varepsilon _0^2{n^3}{h^3}/m{e^4}}} = \frac{{m{e^5}}}{{4\varepsilon _0^2{n^3}{h^3}}} \Rightarrow i\,\,\alpha \,\,{e^5}\)
PHXII12:ATOMS
356473
The ratio of area of first excited state to ground state of orbit of hydrogen atom is
1 \({1: 16}\)
2 \({1: 4}\)
3 \({4: 1}\)
4 \({16: 1}\)
Explanation:
Radius of electron orbit is related with the orbit number as \({r \propto n^{2}}\). \({\therefore}\) Area \({\propto r^{2} \propto n^{4}}\) \({\dfrac{A_{1}}{A_{2}}=\left(\dfrac{n_{1}}{n_{2}}\right)^{4}=\left(\dfrac{2}{1}\right)=\dfrac{16}{1}}\)
KCET - 2024
PHXII12:ATOMS
356474
Statement A : Electrons in the atom are held due to coulomb forces. Statement B : The atom is stable only because the centripetal force due to Coulomb’s law is balanced by the centrifugal force
1 Statement A is correct but Statement B is incorrect.
2 Statement A is incorrect but Statement B is correct.
3 Both Statements are correct.
4 Both Statements are incorrect.
Explanation:
According to postulates of Bohr’s atom model the electron revolves around the nucleus in fixed orbit of definite radii. As long as the electron is in a certain orbit it does not radiate any energy.
PHXII12:ATOMS
356475
The value of ground state energy of a \(H\)-atom is \( - 13.6\,eV\). The energy required to take an electron from ground state to the first excited state is:
Speed of the electron in Bohr’s \(n{\rm{th}}\) orbit is \(v = \frac{{Z{e^2}}}{{2{\varepsilon _0}nh}}\) For \(n = 1,\) \({v_1} = 2.19 \times {10^6}m/s\) For \(n = 2,{v_2} = 1.095 \times {10^6}m/s\) For \(n = 3,{v_3} = 7.3 \times {10^5}m/s\)