Assertion (A): Anode of Coolidge tube gets heated up at time of emission of X-rays.
Reason (R): The anode of Coolidge tube is made of a material of high melting point.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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When high-energy electrons strike the anode in an X-ray tube, most of their kinetic energy (around 99%) is converted into heat, causing the anode to get very hot. So (A) is true. Because of this extreme heating, the anode is made from materials with a high melting point, like Tungsten, to withstand the temperature. So (R) is true. However, (R) describes a design choice made due to the heating, not the explanation for why heating occurs. Hence, (R) is not the correct explanation for (A).
Assertion (A): In H-atom, according to Bohr’s theory, electron revolves around the nucleus in orbits in which the angular momentum of electron is as integral multiple of \(h/(2\pi)\).
Reason (R): Mass of electron is equal to the mass of proton.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Bohr's theory states angular momentum \(L = n h / (2\pi)\). So (A) is true. Mass of electron (\(9.109 \times 10^{-31}\text{ kg}\)) is not equal to mass of proton (\(1.672 \times 10^{-27}\text{ kg}\)). So (R) is false. Hence, (A) is true but (R) is false.
Assertion (A): The ratio of wavelength in first transition of lyman series for H atom and He+ atom is exactly equal to four.
Reason (R): In all atoms electron revolve around fixed nucleus.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The wavelength for hydrogen-like atoms is given by \(1/\lambda \propto Z^2\). For the first transition of the Lyman series (n=1 to n=2), \(lambda_H = 4/(3R)\) and \(lambda_{\text{He}^+} = 1/(3R)\). Their ratio \(lambda_H / \lambda_{\text{He}^+} = 4\). So (A) is true. Reason (R) is false as nuclei are not perfectly fixed; they exhibit recoil and vibration.
Assertion (A): In a Bohr’s atom, frequency of revolution of an electron in its orbit is same as frequency of spectral line, for transition between large quantum numbers.
Reason (R): As Principal quantum number increases in a Bohr’s atom, energy gap between the energy levels decreases.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true due to the correspondence principle where for large \(n\), \(f_{\text{rev}} \propto 1/n^3\) and \(f_{\text{spectral}} \propto 1/n^3\).
Reason (R) is true because \(E_n \propto -1/n^2\), so \(Delta E = |E_{n+1} - E_n| \propto 1/n^3\). Reason (R) correctly explains why the spectral lines become closer, aligning with the classical revolution frequency for large \(n\).
Assertion (A): When the speed of an electron increases its specific charge decreases.
Reason (R): Specific charge is the ratio of the mass to charge.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: relativistic mass \(m = m_0 \sqrt{1-v^2/c^2}\) increases with speed \(v\), so specific charge \(q/m\) decreases. Reason (R) is false because specific charge is defined as the ratio of charge to mass (\(q/m\)), not mass to charge.
Assertion (A): A beam of charged particles is employed in the treatment of cancer.
Reason (R): Charged particles on passing through a material medium lose their energy by causing ionization of the atoms along their path.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true; charged particle therapy (e.g., proton therapy) is used for cancer. Reason (R) is true; charged particles lose energy mainly through ionization, creating a Bragg peak that can precisely damage tumor cells. (R) is the correct explanation for (A).
Assertion (A): Wavelength of Lyman series is less than of Balmer series.
Reason (R): In hydrogen spectrum Balmer series belongs to visible spectrum.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: Lyman series transitions end at \(n=1\) (higher energy, shorter \(lambda\)) while Balmer end at \(n=2\) (lower energy, longer \(\lambda\)).
Reason (R) is true: Balmer lines like \(H_\alpha\) and \(H_\beta\) are in the visible spectrum. However, (R) does not explain why Lyman has shorter wavelengths than Balmer, so it's not the correct explanation.
Assertion (A): The frequency of \(K_\alpha\) X-radiations is greater than \(K_\beta\) for a given target.
Reason (R): \(K_\alpha\) radiation is produced when an electron from \(n = 2\) jumps into the vacancy in \(n = 1\) orbit, whereas in \(K_\beta\) radiation the transition takes place from \(n = 3\) to \(n = 2\).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is false: \(K_\beta\) (\(n=3 \to n=1\)) involves a larger energy difference than \(K_\alpha\) (\(n=2 \to n=1\)), so \(f_{K_\beta}\ > f_{K_\alpha}\). Reason (R) is false: While \(K_\alpha\) is \(n=2 \to n=1\), \(K_\beta\) is \(n=3 \to n=1\), not \(n=3 \to n=2\). Both are false.
Assertion (A): Frequency of characteristic X-ray will change if atomic number of target is changed.
Reason (R): When high energy electron strikes on target then characteristics and continuous X-rays are emitted.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: Characteristic X-ray frequency depends on the atomic number \(Z\) of the target (Moseley's Law, \(f \propto (Z-b)^2\)). Reason (R) is true: Both characteristic and continuous X-rays are emitted during electron bombardment. However, (R) describes the emission process generally, not the \(Z\)-dependence of characteristic X-ray frequency, so it's not the correct explanation.
Assertion (A): A hydrogen atom can absorb a photon whose energy is greater than \(13.6\text{ eV}\).
Reason (R): The binding energy of a hydrogen atom is \(13.6\text{ eV}\).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Binding energy of hydrogen atom is \(13.6\text{ eV}\). A photon with energy \(ge 13.6\text{ eV}\) can ionize the atom. Excess energy becomes \(K.E.\) of electron. So (A) is true. (R) states the binding energy. (R) correctly explains (A).