The radius of inner most orbit of a hydrogen atom is \(5.3 \times 10^{-11}\) m. What is the radius of the third allowed orbit of a hydrogen atom?
1. \(4.77~ \mathring{A}\) 2. \(0.53~ \mathring{A}\)
3. \(1.06~ \mathring{A}\) 4. \(1.59~ \mathring{A}\)
Subtopic:  Bohr's Model of Atom |
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NEET - 2023
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The ground state energy of a hydrogen atom is \(-13.6~\text{eV}\). The energy needed to ionize the hydrogen atom from its second excited state will be:
1. \(13.6~\text{eV}\)
2. \(6.8~\text{eV}\)
3. \(1.51~\text{eV}\)
4. \(3.4~\text{eV}\)
Subtopic:  Bohr's Model of Atom |
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NEET - 2023
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The angular momentum of an electron moving in an orbit of a hydrogen atom is \(1.5\Big(\frac h\pi\Big).\) The energy in the same orbit is nearly:
1. \(-1.5~\text{eV}\)
2. \(-1.6~\text{eV}\)
3. \(-1.3~\text{eV}\)
4. \(-1.4~\text{eV}\)
Subtopic:  Bohr's Model of Atom |
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Let \(T_1\) and \(T_2\) be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to Bohr's model of an atom, the ratio \(T_1:T_2\) is:
1. \(9:4\)
2. \(1:4\)
3. \(4:1\)
4. \(4:9\) 
Subtopic:  Bohr's Model of Atom |
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NEET - 2022
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Let \(L_1\) and \(L_2\) be the orbital angular momentum of an electron in the first and second excited states of the hydrogen atom, respectively. According to Bohr's model, the ratio \(L_1:L_2\) is:
1. \(1:2\)
2. \(2:1\)
3. \(3:2\)
4. \(2:3\)

Subtopic:  Bohr's Model of Atom |
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Let \(R_1\) be the radius of the second stationary orbit and \(R_2\) be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio \(\frac{R_1}{R_2}\) is:
1. \(0.25\)
2. \(0.5\)
3. \(2\)
4. \(4\)
Subtopic:  Bohr's Model of Atom |
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For which one of the following Bohr model is not valid?

1. Singly ionised helium atom \(He^{+}\)
2. Deuteron atom
3. Singly ionised neon atom \(Ne^{+}\)
4. Hydrogen atom
Subtopic:  Bohr's Model of Atom |
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The total energy of an electron in the \(n^{th}\) stationary orbit of the hydrogen atom can be obtained by:
1. \(E_n = \frac{13.6}{n^2}~\text{eV}\)
2. \(E_n = -\frac{13.6}{n^2}~\text{eV}\)
3. \(E_n = \frac{1.36}{n^2}~\text{eV}\)
4. \(E_n = -{13.6}\times{n^2}~\text{eV}\)

Subtopic:  Bohr's Model of Atom |
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The total energy of an electron in the orbit of an atom is \(-3.4~\mathrm{eV}\). Its kinetic and potential energies are, respectively:

1. \(3.4~\mathrm{eV},~3.4~\mathrm{eV}\)
2. \(-3.4~\mathrm{eV},~-3.4~\mathrm{eV}\)
3. \(-3.4~\mathrm{eV},~-6.8~\mathrm{eV}\)
4. \(3.4~\mathrm{eV},~-6.8~\mathrm{eV}\)
Subtopic:  Bohr's Model of Atom |
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The radius of the first permitted Bohr orbit for the electron in a hydrogen atom equals \(0.5~\mathring{{A}}\) and its ground state energy equals \(-13.6~\text{eV}\). If the electron in the hydrogen atom is replaced by a muon \((\mu^{-})\) [charge same as electron and mass \(207~m_e\)], the first Bohr radius and ground state energy will be: ( \(m_e\) represents the mass of an electron)
1. \(0.53\times10^{-13}~\text{m}, ~-3.6~\text{eV}\)
2. \(25.6\times10^{-13}~\text{m}, ~-2.8~\text{eV}\)
3. \(2.56\times10^{-13}~\text{m}, ~-2.8~\text{keV}\)
4. \(2.56\times10^{-13}~\text{m}, ~-13.6~\text{eV}\)
Subtopic:  Bohr's Model of Atom |
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