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In the Bohr model of \(\mathrm{H\text-}\)atom, an electron \((e)\) is revolving around a proton \((p)\) with velocity \(v\). If \(r\) is the radius of the orbit, \(m\) is the mass and \(\varepsilon_0\) is vacuum permittivity, then the value of \(v\) is:
1. \(\frac{e}{\sqrt{4\pi m\varepsilon_0 r}}\)
2. \(\frac{2e}{\sqrt{\pi m\varepsilon_0 r}}\)
3. \(\frac{e}{\sqrt{\pi m\varepsilon_0 r}}\)
4. \(\frac{e}{4\pi m\varepsilon_0 r}\)
1. \(\frac{e}{\sqrt{4\pi m\varepsilon_0 r}}\)
2. \(\frac{2e}{\sqrt{\pi m\varepsilon_0 r}}\)
3. \(\frac{e}{\sqrt{\pi m\varepsilon_0 r}}\)
4. \(\frac{e}{4\pi m\varepsilon_0 r}\)
Subtopic: Â Bohr's Model of Atom |
 74%
Level 2: 60%+
AIPMT - 1998
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Maximum frequency of emission is obtained for the transition:
1. n = 2 to n = 1
2. n = 6 to n = 2
3. n = 1 to n = 2
4. n = 2 to n = 6
Subtopic: Â Bohr's Model of Atom |
 61%
Level 2: 60%+
AIPMT - 2000
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Subtopic: Â Bohr's Model of Atom |
 83%
Level 1: 80%+
AIPMT - 2000
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When an electron transitions from \(n=4\) to \(n=2,\) then the emitted line in the spectrum will be:
| 1. | the first line of the Lyman series. |
| 2. | the second line of the Balmer series. |
| 3. | the first line of the Paschen series. |
| 4. | the second line of the Paschen series. |
Subtopic: Â Spectral Series |
 87%
Level 1: 80%+
AIPMT - 2000
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If the energy of the hydrogen atom in \(n^{\text{th}}\) orbit is \(E_n,\) then the energy in \(n^{\text{th}}\) orbit of the singly ionised helium atom will be:
| 1. | \(4E_n\) | 2. | \(\dfrac{E_n}{4}\) |
| 3. | \(2E_n\) | 4. | \(\dfrac{E_n}{2}\) |
Subtopic: Â Bohr's Model of Atom |
 78%
Level 2: 60%+
AIPMT - 2001
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An electron is moving around the nucleus of a hydrogen atom in a circular orbit of radius \(r\). What is the coulomb force \(\vec {F}\) between the two? \(\left ( \text{where},K=\frac{1}{4\pi \epsilon _{0}} \right )\)
1. \(K \frac{e^{2}}{r^{2}} \hat{r}\)
2. \(- K \frac{e^{2}}{r^{3}} \hat{r}\)
3. \(K \frac{e^{2}}{r^{3}} \overset{\rightarrow}{r}\)
4. \(- K \frac{e^{2}}{r^{3}} \overset{\rightarrow}{r}\)
1. \(K \frac{e^{2}}{r^{2}} \hat{r}\)
2. \(- K \frac{e^{2}}{r^{3}} \hat{r}\)
3. \(K \frac{e^{2}}{r^{3}} \overset{\rightarrow}{r}\)
4. \(- K \frac{e^{2}}{r^{3}} \overset{\rightarrow}{r}\)
Subtopic: Â Various Atomic Models |
 56%
Level 3: 35%-60%
AIPMT - 2003
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In which of the following systems will the radius of the first orbit (\(n=1\)) be minimum:
1. doubly ionized lithium
2. singly ionized helium
3. deuterium atom
4. hydrogen atom
Subtopic: Â Bohr's Model of Atom |
 73%
Level 2: 60%+
AIPMT - 2003
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Energy \(E\) of a hydrogen atom with principal quantum number \(n\) is given by \(E=-\frac{13.6}{n^{2}}~\text{eV}.\) The energy of a photon ejected when the electron jumps from \(n=3\) state to \(n=2\) state of hydrogen is approximately:
1. \(0.85~\text{eV}\)
2. \(3.4~\text{eV}\)
3. \(1.9~\text{eV}\)
4. \(1.5~\text{eV}\)
Subtopic: Â Bohr's Model of Atom |
 79%
Level 2: 60%+
AIPMT - 2004
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The Bohr model of atoms:
| 1. | uses Einstein's photoelectric equation. |
| 2. | predicts continuous emission spectra for atoms. |
| 3. | predicts the same emission spectra for all types of atoms. |
| 4. | assumes that the angular momentum of electrons is quantized. |
Subtopic: Â Bohr's Model of Atom |
 83%
Level 1: 80%+
AIPMT - 2004
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The total energy of an electron in the first excited state of a hydrogen atom is about \(-3.4~\text{eV}.\) Its kinetic energy in this state will be:
1. \(-6.8~\text{eV}\)
2. \(3.4~\text{eV}\)
3. \(6.8~\text{eV}\)
4. \(-3.4~\text{eV}\)
Subtopic: Â Bohr's Model of Atom |
 86%
Level 1: 80%+
AIPMT - 2005
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