Bohr Model of the Hydrogen Atom
« Previous Topic: Atomic Collisions Next Topic: De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation »
PHXII12:ATOMS

356425 The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the \(5^{\text {th }}\) excited state of a hydrogen atom is

1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 1
JEE - 2024
PHXII12:ATOMS

356426 The binding energy of a \(H\)-atom, considering an electron moving around a fixed nuclei (proton), is \(B = \frac{{m{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(m\)- mass of electron). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be \(B = - \frac{{M{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(M = \) proton mass). This last expression is not correct because

1 The frame in which the electron is at rest is not inertial.
2 Bohr-quantisation applies only to electron
3 \(n\) would not be integral
4 The motion of the proton would not be in circular orbits, even approximately.
NCERT Exemplar
PHXII12:ATOMS

356427 Frequency of revolution of an electron revolving in \({n^{th}}\) orbit of \(H\) - atom is proportional to

1 \(n\) independent of \(n\)
2 \(1/{n^2}\)
3 \(1/{n^3}\)
4 \(n\)
KCET - 2019
PHXII12:ATOMS

356428 Assertion :
In a hydrogen atom energy of emitted photon corresponding to transition from \(n=2\) to \(n=1\) is much greater as compared to transition from \(n=\infty\) to \(n=2\).
Reason :
Wavelength of photon is directly proportional to the energy of emitted photon.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII12:ATOMS

356429 According to Bohr’s theory, the expressions for the kinetic and potential energy of an electron revolving in an orbit is given respectively by

1 \( + \frac{{8\pi {\varepsilon _0}{e^2}}}{r}{\rm{and}} - \frac{{4\pi {\varepsilon _0}{e^2}}}{r}\)
2 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and}} - \frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
3 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and + }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
4 \( - \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{ and - }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
Join With Us for More Updates
PHXII12:ATOMS

356425 The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the \(5^{\text {th }}\) excited state of a hydrogen atom is

1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 1
JEE - 2024
PHXII12:ATOMS

356426 The binding energy of a \(H\)-atom, considering an electron moving around a fixed nuclei (proton), is \(B = \frac{{m{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(m\)- mass of electron). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be \(B = - \frac{{M{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(M = \) proton mass). This last expression is not correct because

1 The frame in which the electron is at rest is not inertial.
2 Bohr-quantisation applies only to electron
3 \(n\) would not be integral
4 The motion of the proton would not be in circular orbits, even approximately.
NCERT Exemplar
PHXII12:ATOMS

356427 Frequency of revolution of an electron revolving in \({n^{th}}\) orbit of \(H\) - atom is proportional to

1 \(n\) independent of \(n\)
2 \(1/{n^2}\)
3 \(1/{n^3}\)
4 \(n\)
KCET - 2019
PHXII12:ATOMS

356428 Assertion :
In a hydrogen atom energy of emitted photon corresponding to transition from \(n=2\) to \(n=1\) is much greater as compared to transition from \(n=\infty\) to \(n=2\).
Reason :
Wavelength of photon is directly proportional to the energy of emitted photon.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII12:ATOMS

356429 According to Bohr’s theory, the expressions for the kinetic and potential energy of an electron revolving in an orbit is given respectively by

1 \( + \frac{{8\pi {\varepsilon _0}{e^2}}}{r}{\rm{and}} - \frac{{4\pi {\varepsilon _0}{e^2}}}{r}\)
2 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and}} - \frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
3 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and + }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
4 \( - \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{ and - }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
For More Updates join with Us
PHXII12:ATOMS

356425 The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the \(5^{\text {th }}\) excited state of a hydrogen atom is

1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 1
JEE - 2024
PHXII12:ATOMS

356426 The binding energy of a \(H\)-atom, considering an electron moving around a fixed nuclei (proton), is \(B = \frac{{m{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(m\)- mass of electron). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be \(B = - \frac{{M{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(M = \) proton mass). This last expression is not correct because

1 The frame in which the electron is at rest is not inertial.
2 Bohr-quantisation applies only to electron
3 \(n\) would not be integral
4 The motion of the proton would not be in circular orbits, even approximately.
NCERT Exemplar
PHXII12:ATOMS

356427 Frequency of revolution of an electron revolving in \({n^{th}}\) orbit of \(H\) - atom is proportional to

1 \(n\) independent of \(n\)
2 \(1/{n^2}\)
3 \(1/{n^3}\)
4 \(n\)
KCET - 2019
PHXII12:ATOMS

356428 Assertion :
In a hydrogen atom energy of emitted photon corresponding to transition from \(n=2\) to \(n=1\) is much greater as compared to transition from \(n=\infty\) to \(n=2\).
Reason :
Wavelength of photon is directly proportional to the energy of emitted photon.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII12:ATOMS

356429 According to Bohr’s theory, the expressions for the kinetic and potential energy of an electron revolving in an orbit is given respectively by

1 \( + \frac{{8\pi {\varepsilon _0}{e^2}}}{r}{\rm{and}} - \frac{{4\pi {\varepsilon _0}{e^2}}}{r}\)
2 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and}} - \frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
3 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and + }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
4 \( - \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{ and - }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
NEET DIGITAL LIBRARY
PHXII12:ATOMS

356425 The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the \(5^{\text {th }}\) excited state of a hydrogen atom is

1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 1
JEE - 2024
PHXII12:ATOMS

356426 The binding energy of a \(H\)-atom, considering an electron moving around a fixed nuclei (proton), is \(B = \frac{{m{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(m\)- mass of electron). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be \(B = - \frac{{M{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(M = \) proton mass). This last expression is not correct because

1 The frame in which the electron is at rest is not inertial.
2 Bohr-quantisation applies only to electron
3 \(n\) would not be integral
4 The motion of the proton would not be in circular orbits, even approximately.
NCERT Exemplar
PHXII12:ATOMS

356427 Frequency of revolution of an electron revolving in \({n^{th}}\) orbit of \(H\) - atom is proportional to

1 \(n\) independent of \(n\)
2 \(1/{n^2}\)
3 \(1/{n^3}\)
4 \(n\)
KCET - 2019
PHXII12:ATOMS

356428 Assertion :
In a hydrogen atom energy of emitted photon corresponding to transition from \(n=2\) to \(n=1\) is much greater as compared to transition from \(n=\infty\) to \(n=2\).
Reason :
Wavelength of photon is directly proportional to the energy of emitted photon.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII12:ATOMS

356429 According to Bohr’s theory, the expressions for the kinetic and potential energy of an electron revolving in an orbit is given respectively by

1 \( + \frac{{8\pi {\varepsilon _0}{e^2}}}{r}{\rm{and}} - \frac{{4\pi {\varepsilon _0}{e^2}}}{r}\)
2 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and}} - \frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
3 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and + }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
4 \( - \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{ and - }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
Join With Us for More Updates
PHXII12:ATOMS

356425 The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the \(5^{\text {th }}\) excited state of a hydrogen atom is

1 \(\dfrac{1}{2}\)
2 4
3 \(\dfrac{1}{4}\)
4 1
JEE - 2024
PHXII12:ATOMS

356426 The binding energy of a \(H\)-atom, considering an electron moving around a fixed nuclei (proton), is \(B = \frac{{m{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(m\)- mass of electron). If one decides to work in a frame of reference where the electron is at rest, the proton would be moving around it. By similar arguments, the binding energy would be \(B = - \frac{{M{e^4}}}{{8{n^2}\varepsilon _0^2{h^2}}} \cdot \) (\(M = \) proton mass). This last expression is not correct because

1 The frame in which the electron is at rest is not inertial.
2 Bohr-quantisation applies only to electron
3 \(n\) would not be integral
4 The motion of the proton would not be in circular orbits, even approximately.
NCERT Exemplar
PHXII12:ATOMS

356427 Frequency of revolution of an electron revolving in \({n^{th}}\) orbit of \(H\) - atom is proportional to

1 \(n\) independent of \(n\)
2 \(1/{n^2}\)
3 \(1/{n^3}\)
4 \(n\)
KCET - 2019
PHXII12:ATOMS

356428 Assertion :
In a hydrogen atom energy of emitted photon corresponding to transition from \(n=2\) to \(n=1\) is much greater as compared to transition from \(n=\infty\) to \(n=2\).
Reason :
Wavelength of photon is directly proportional to the energy of emitted photon.

1 Both Assertion and Reason are correct and Reason is the correct explanation of the Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of the Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
PHXII12:ATOMS

356429 According to Bohr’s theory, the expressions for the kinetic and potential energy of an electron revolving in an orbit is given respectively by

1 \( + \frac{{8\pi {\varepsilon _0}{e^2}}}{r}{\rm{and}} - \frac{{4\pi {\varepsilon _0}{e^2}}}{r}\)
2 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and}} - \frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
3 \( + \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{and + }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)
4 \( - \frac{{{e^2}}}{{8\pi {\varepsilon _0}r}}{\rm{ and - }}\frac{{{e^2}}}{{4\pi {\varepsilon _0}r}}\)