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Q. No.Instead of angular momentum quantization, a student posits that energy is quantized as \(E=-\dfrac{E_{0}}{n}~\left ( E_{0}>0 \right )\) and \(n\) is a positive integer. Which of the following options is correct?
1.
the radius of the electron orbit is \(r\propto\sqrt n\).
2.
the speed of the electron is \(v\propto\sqrt n\).
3.
the angular speed of the electron is \(\omega\propto 1/n\).
4.
the angular momentum of the electron is \(\propto\sqrt n\).
Subtopic: Bohr's Model of Atom |
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The ratio of the speed of the electron in the \(3^{\mathrm{rd}}\) orbit of \(\mathrm{He}^{+}\) to the speed of the electron in the \(3^{\mathrm{rd}}\) orbit of the hydrogen atom will be:
1. \(1:1\)
2. \(1:2\)
3. \(4:1\)
4. \(2:1\)
1. \(1:1\)
2. \(1:2\)
3. \(4:1\)
4. \(2:1\)
Subtopic: Bohr's Model of Atom |
72%
From NCERT
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A hypothetical function defined as \(Y_n=(E_n-E_{n-1})\) where \(E_n\) is the total energy of an orbit of hydrogen atom having principal quantum number \(n,\) then:
1. \(Y_2>Y_3\)
2. \(Y_2<Y_3\)
3. \(Y_2=Y_3\)
4. \(2Y_2=Y_3\)
1. \(Y_2>Y_3\)
2. \(Y_2<Y_3\)
3. \(Y_2=Y_3\)
4. \(2Y_2=Y_3\)
Subtopic: Bohr's Model of Atom |
69%
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Consider an electron revolving around nucleus in an orbit. \((KE)\) denotes its kinetic energy, \((PE)\) denotes potential energy of electron-nucleus system and \((TE)\) denotes total energy of electron-nucleus system. The value of \(\left|\dfrac{(KE)+(TE)}{(PE)}\right|\) is equal to:
1. \(0\)
2. \(1\)
3. \(2\)
4. \(3\)
1. \(0\)
2. \(1\)
3. \(2\)
4. \(3\)
Subtopic: Bohr's Model of Atom |
71%
From NCERT
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In which of the following systems will be wavelength corresponding to \(n=3\) to \(n=1\) be minimum?
1. Hydrogen atom
2. Deuterium atom
3. Singly ionized helium
4. Doubly ionized lithium
1. Hydrogen atom
2. Deuterium atom
3. Singly ionized helium
4. Doubly ionized lithium
Subtopic: Spectral Series |
76%
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The transition from the state \(n= 4~\text{to}~n=3\) in hydrogen-like atoms results in ultraviolet radiation. Infrared radiation will be obtained in the transition:
1. \(2\rightarrow1\)
2. \(3\rightarrow2\)
3. \(4\rightarrow2\)
4. \(5\rightarrow4\)
1. \(2\rightarrow1\)
2. \(3\rightarrow2\)
3. \(4\rightarrow2\)
4. \(5\rightarrow4\)
Subtopic: Spectral Series |
77%
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Given below are two statements:
| Statement I: | The scattering of α-particles at large angles is primarily due to the atomic nucleus. |
| Statement II: | The atomic nucleus is very heavy in comparison to electrons. |
| 1. | Statement I is correct and Statement II is incorrect. |
| 2. | Statement I is incorrect and Statement II is correct. |
| 3. | Both Statement I and Statement II are correct. |
| 4. | Both Statement I and Statement II are incorrect. |
Subtopic: Various Atomic Models |
80%
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The product of the angular momentum and the kinetic energy of an electron in the \(n^\text{th}\) Bohr orbit in a hydrogen atom is proportional to:
1.
\(n\)
2.
\(n^2\)
3.
\(\dfrac1n\)
4.
\(\dfrac{1}{n^3}\)
Subtopic: Bohr's Model of Atom |
77%
From NCERT
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Given below are two statements:
| Assertion (A): | The positively charged nucleus of an atom has a radius of almost \(10^{-15}~\text{m}\). |
| Reason (R): | In \(\alpha\)-particle scattering experiment, the distance of the closest approach for \(\alpha\)-particle is \(\approx 10^{-15}~\text m\). |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | Both (A) and (R) are False. |
Subtopic: Various Atomic Models |
58%
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Let \(T_1\) and \(T_2\) be the energy of an electron in the first and second excited states of the 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. \(4:9\)
1. \(9:4\)
2. \(1:4\)
3. \(4:1\)
4. \(4:9\)
Subtopic: Bohr's Model of Atom |
68%
From NCERT
NEET - 2022
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