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. \(\frac{e}{4\pi m\varepsilon_0 r}\)

Subtopic:  Bohr's Model of Atom |
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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:  Bohr's Model of Atom |
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The life span of atomic hydrogen is:

1. Fraction of one sec

2. One year

3. One hour

4. One day

Subtopic:  Bohr's Model of Atom |
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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:  Spectral Series |
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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:  Bohr's Model of Atom |
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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. \(- K \frac{e^{2}}{r^{3}} \overset{\rightarrow}{r}\)
Subtopic:  Various Atomic Models |
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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:  Bohr's Model of Atom |
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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:  Bohr's Model of Atom |
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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:  Bohr's Model of Atom |
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The total energy of an electron in the first excited state of a hydrogen atom is about \(-3.4\) 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:  Bohr's Model of Atom |
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