If an alpha nucleus of energy \(\frac{1}{2}mv^2\) bombards a heavy nuclear target of charge \(Ze\), then the distance of closest approach for the alpha nucleus will be proportional to:
1. \(\frac{1}{Ze} \) 2. \(v^2 \)
3. \(\frac{1}{m} \) 4. \(\frac{1}{v^4}\)

Subtopic:  Various Atomic Models |
 83%
From NCERT
AIPMT - 2010
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The ratio of the longest wavelengths corresponding to the Lyman and Balmer series in the hydrogen spectrum is:
1. \(\frac{3}{23}\) 2. \(\frac{7}{29}\)
3. \(\frac{9}{31}\) 4. \(\frac{5}{27}\)
Subtopic:  Spectral Series |
 88%
From NCERT
AIPMT - 2013
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Given that the value of the Rydberg constant is \(10^{7}~\text{m}^{-1}\), what will be the wave number of the last line of the Balmer series in the hydrogen spectrum?
1. \(0.5 \times 10^{7}~\text{m}^{-1}\)
2. \(0.25 \times 10^{7} ~\text{m}^{-1}\)
3. \(2.5 \times 10^{7}~\text{m}^{-1}\)
4. \(0.025 \times 10^{4} ~\text{m}^{-1}\)

Subtopic:  Spectral Series |
 86%
From NCERT
NEET - 2016
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The ratio of the total acceleration of the electron in a singly ionised helium atom and a hydrogen atom (both in the ground state) is:
1. \(1\)
2. \(8\)
3. \(4\)
4. \(16\)

Subtopic:  Bohr's Model of Atom |
 53%
From NCERT
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An electron revolves around a nucleus of charge \(Ze\). In order to excite the electron from the state \(n=3\) to \(n=4\), the energy required is \(66.0 ~\text{eV}\). The value of \(Z\) will be:
1. \(25\)
2. \(10\)
3. \(4\)
4. \(5\)

Subtopic:  Bohr's Model of Atom |
 66%
From NCERT
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How much is the total energy of an electron in the first orbit of a hydrogen atom equal to?
1. total energy of electron in \(1\text{st}\) orbit of \(\mathrm{He}^{+}\)
2. total energy of electron in \(3\text{rd}\) orbit of \(\mathrm{He}^{+}\)
3. total energy of electron in \(2\text{nd}\) orbit of \(\mathrm{Li}^{++}\)
4. total energy of electron in \(3\text{rd}\) orbit of \(\mathrm{Li}^{++}\)

Subtopic:  Bohr's Model of Atom |
 72%
From NCERT
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The electric potential between a proton and an electron is given by \(V = V_0\mathrm{Ln}\left(\frac{r}{r_0}\right)\) where \(r_0\) is a constant. Assuming Bohr’s model to be applicable, the variation of \(r_n\) with \(n\), \(n\) being the principal quantum number, is:
1. \(r_n \propto n\)
2. \(r_n \propto\frac{1}{n}\)
3. \(r_n\propto n^2\)
4. \(r_n \propto\frac{1}{n^2}\)

Subtopic:  Bohr's Model of Atom |
From NCERT
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In a hypothetical Bohr hydrogen, the mass of the electron is doubled. What will be the energy \(E_0\) and the radius \(r_0\) of the first orbit?
\((a_0\) is the Bohr radius) 
1. \(E_0=-27.2 ~\text{eV};~r_0={a}_0 / 2\)
2. \(E_0=-27.2 ~\text{eV}; ~r_0={a}_0\)
3. \(E_0=-13.6~\text{eV} ; ~r_0={a}_0 / 2\)
4. \(E_0=-13.6 ~\text{eV}; ~r_0={a}_0\)

Subtopic:  Bohr's Model of Atom |
 54%
From NCERT
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What is the ratio of the longest to shortest wavelengths in Brackett series of hydrogen spectra?
1. \(\dfrac{25}{9}\) 2. \(\dfrac{17}{6}\)
3. \(\dfrac{9}{5}\) 4. \(\dfrac{4}{3}\)
Subtopic:  Spectral Series |
 79%
From NCERT
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What is the ratio of the largest to shortest wavelengths in the Lyman series of hydrogen spectra?
1. \(\dfrac{25}{9}\) 2. \(\dfrac{17}{6}\)
3. \(\dfrac{9}{5}\) 4. \(\dfrac{4}{3}\)
Subtopic:  Spectral Series |
 82%
From NCERT
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