Assertion (A): If the accelerating potential in an X-ray tube is increased, the wavelength of the characteristic X-rays does not change.
Reason (R): When an electron beam strikes the target in an X-ray tube, part of the kinetic energy is converted into X-ray energy.
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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Characteristic X-rays depend on the target material's atomic structure, not the accelerating potential. So (A) is true. X-rays are produced when electron kinetic energy is converted to electromagnetic radiation.
So (R) is true. However, (R) describes the general process of X-ray production, not why characteristic wavelengths are independent of accelerating potential. Hence, (R) is not the correct explanation for (A).
Assertion (A): It is essential that all the lines available in the emission spectrum will also be available in the absorption spectrum.
Reason (R): The spectrum of hydrogen atom is only absorption 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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Absorption lines generally correspond to transitions from the ground state, while emission lines can originate from any excited state. Thus, not all emission lines are necessarily absorption lines (A) is false. Hydrogen atoms can produce both emission and absorption spectra. Thus, (R) is false. Therefore, both (A) and (R) are false.
Assertion (A): Bohr postulates that the electrons in stationary orbits around the nucleus do not radiate.
Reason (R): According to classical physics all moving electrons radiate.
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 first postulate (A) states that electrons in stationary orbits do not radiate energy. This postulate was introduced to address the classical physics problem (R) where accelerating charged particles, like orbiting electrons, should continuously radiate energy.
Thus, both (A) and (R) are true, and (R) provides the underlying classical paradox that Bohr's postulate (A) resolved.
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): 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): 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): 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
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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).
Assertion (A): A welder uses mouth mask for protection of eyes.
Reason (R): Welding arc produces X-rays.
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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Welders use face masks for eye protection from intense UV/Visible/IR radiation and sparks. So (A) is true. Welding arcs primarily emit strong UV radiation, not X-rays, as the main hazard. So (R) is false.