Bohr Model of the Hydrogen Atom
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PHXII12:ATOMS

356417 The electron of hydrogen atom is considered to be revolving round a proton in circular orbit of radius \(\hbar^{2} / m e^{2}\) with velocity \(e^{2} / \hbar\), where \(\hbar=h / 2 \pi\). The current \(i\) is

1 \(\dfrac{4 \pi^{2} m e^{5}}{h^{2}}\)
2 \(\dfrac{4 \pi^{2} m e^{5}}{h^{3}}\)
3 \(\dfrac{4 \pi^{2} m^{2} e^{2}}{h^{3}}\)
4 \(\dfrac{4 \pi^{2} m^{2} e^{5}}{h^{3}}\)
PHXII12:ATOMS

356418 An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The coulomb force \({\vec F}\) between the two is

1 \(K\frac{{{e^2}}}{{{r^2}}}\vec r\)
2 \( - K\frac{{{e^2}}}{{{r^3}}}\vec r\)
3 \(K\frac{{{e^2}}}{{{r^3}}}\hat r\)
4 \( - K\frac{{{e^2}}}{{{r^2}}}\hat r\)
PHXII12:ATOMS

356419 If the radius of first Bohr orbit is \(r\), then radius of second orbit will be

1 \(2r\)
2 \(\frac{r}{2}\)
3 \(4r\)
4 \(\sqrt {2r} \)
PHXII12:ATOMS

356420 An electron in a hydrogen atom makes a transition from \(n=n_{1}\) to \(n=n_{2}\). The time period of the electron in the initial state is eight times that in the final state. The possible values of \(n_{1}\) and \(n_{2}\) are:

1 \(n_{1}=4, n_{2}=2\)
2 \(n_{1}=8, n_{2}=2\)
3 \(n_{1}=8, n_{2}=1\)
4 \(n_{1}=6, n_{2}=2\)
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PHXII12:ATOMS

356417 The electron of hydrogen atom is considered to be revolving round a proton in circular orbit of radius \(\hbar^{2} / m e^{2}\) with velocity \(e^{2} / \hbar\), where \(\hbar=h / 2 \pi\). The current \(i\) is

1 \(\dfrac{4 \pi^{2} m e^{5}}{h^{2}}\)
2 \(\dfrac{4 \pi^{2} m e^{5}}{h^{3}}\)
3 \(\dfrac{4 \pi^{2} m^{2} e^{2}}{h^{3}}\)
4 \(\dfrac{4 \pi^{2} m^{2} e^{5}}{h^{3}}\)
PHXII12:ATOMS

356418 An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The coulomb force \({\vec F}\) between the two is

1 \(K\frac{{{e^2}}}{{{r^2}}}\vec r\)
2 \( - K\frac{{{e^2}}}{{{r^3}}}\vec r\)
3 \(K\frac{{{e^2}}}{{{r^3}}}\hat r\)
4 \( - K\frac{{{e^2}}}{{{r^2}}}\hat r\)
PHXII12:ATOMS

356419 If the radius of first Bohr orbit is \(r\), then radius of second orbit will be

1 \(2r\)
2 \(\frac{r}{2}\)
3 \(4r\)
4 \(\sqrt {2r} \)
PHXII12:ATOMS

356420 An electron in a hydrogen atom makes a transition from \(n=n_{1}\) to \(n=n_{2}\). The time period of the electron in the initial state is eight times that in the final state. The possible values of \(n_{1}\) and \(n_{2}\) are:

1 \(n_{1}=4, n_{2}=2\)
2 \(n_{1}=8, n_{2}=2\)
3 \(n_{1}=8, n_{2}=1\)
4 \(n_{1}=6, n_{2}=2\)
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PHXII12:ATOMS

356417 The electron of hydrogen atom is considered to be revolving round a proton in circular orbit of radius \(\hbar^{2} / m e^{2}\) with velocity \(e^{2} / \hbar\), where \(\hbar=h / 2 \pi\). The current \(i\) is

1 \(\dfrac{4 \pi^{2} m e^{5}}{h^{2}}\)
2 \(\dfrac{4 \pi^{2} m e^{5}}{h^{3}}\)
3 \(\dfrac{4 \pi^{2} m^{2} e^{2}}{h^{3}}\)
4 \(\dfrac{4 \pi^{2} m^{2} e^{5}}{h^{3}}\)
PHXII12:ATOMS

356418 An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The coulomb force \({\vec F}\) between the two is

1 \(K\frac{{{e^2}}}{{{r^2}}}\vec r\)
2 \( - K\frac{{{e^2}}}{{{r^3}}}\vec r\)
3 \(K\frac{{{e^2}}}{{{r^3}}}\hat r\)
4 \( - K\frac{{{e^2}}}{{{r^2}}}\hat r\)
PHXII12:ATOMS

356419 If the radius of first Bohr orbit is \(r\), then radius of second orbit will be

1 \(2r\)
2 \(\frac{r}{2}\)
3 \(4r\)
4 \(\sqrt {2r} \)
PHXII12:ATOMS

356420 An electron in a hydrogen atom makes a transition from \(n=n_{1}\) to \(n=n_{2}\). The time period of the electron in the initial state is eight times that in the final state. The possible values of \(n_{1}\) and \(n_{2}\) are:

1 \(n_{1}=4, n_{2}=2\)
2 \(n_{1}=8, n_{2}=2\)
3 \(n_{1}=8, n_{2}=1\)
4 \(n_{1}=6, n_{2}=2\)
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PHXII12:ATOMS

356417 The electron of hydrogen atom is considered to be revolving round a proton in circular orbit of radius \(\hbar^{2} / m e^{2}\) with velocity \(e^{2} / \hbar\), where \(\hbar=h / 2 \pi\). The current \(i\) is

1 \(\dfrac{4 \pi^{2} m e^{5}}{h^{2}}\)
2 \(\dfrac{4 \pi^{2} m e^{5}}{h^{3}}\)
3 \(\dfrac{4 \pi^{2} m^{2} e^{2}}{h^{3}}\)
4 \(\dfrac{4 \pi^{2} m^{2} e^{5}}{h^{3}}\)
PHXII12:ATOMS

356418 An electron is moving round the nucleus of a hydrogen atom in a circular orbit of radius \(r\). The coulomb force \({\vec F}\) between the two is

1 \(K\frac{{{e^2}}}{{{r^2}}}\vec r\)
2 \( - K\frac{{{e^2}}}{{{r^3}}}\vec r\)
3 \(K\frac{{{e^2}}}{{{r^3}}}\hat r\)
4 \( - K\frac{{{e^2}}}{{{r^2}}}\hat r\)
PHXII12:ATOMS

356419 If the radius of first Bohr orbit is \(r\), then radius of second orbit will be

1 \(2r\)
2 \(\frac{r}{2}\)
3 \(4r\)
4 \(\sqrt {2r} \)
PHXII12:ATOMS

356420 An electron in a hydrogen atom makes a transition from \(n=n_{1}\) to \(n=n_{2}\). The time period of the electron in the initial state is eight times that in the final state. The possible values of \(n_{1}\) and \(n_{2}\) are:

1 \(n_{1}=4, n_{2}=2\)
2 \(n_{1}=8, n_{2}=2\)
3 \(n_{1}=8, n_{2}=1\)
4 \(n_{1}=6, n_{2}=2\)
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