Assertion (A): If the accelerating potential of a X-Ray tube is increased then the characteristic wavelength decreases.
Reason (R): The cut-off wavelength for a X-Ray tube is given by \(\lambda_{\text{min}} = \frac{hc}{eV}\), where \(V\) is accelerating potential.
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 wavelength depends on target material, not accelerating potential. However, if 'characteristic wavelength' in (A) refers to 'cut-off wavelength', then \(\lambda_{\text{min}} = hc/(eV)\) implies increasing \(V\) decreases \(\lambda_{\text{min}}\). Under this interpretation, (A) is true, and (R) is true and explains (A).
Assertion (A): Cut-off wavelength of x-ray is independent of type of target metal
Reason (R): Wavelength of \(K_{alpha}\) x-ray depends upon type of target metal.
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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Concept: X-ray production mechanisms.
Formula: Cut-off wavelength \(\lambda_{\text{min}} = \frac{hc}{eV}\) (depends on voltage). Characteristic X-ray energy \(E = h\nu\) (depends on atomic transitions).
Solution: The cut-off (minimum) wavelength of continuous X-rays depends only on the accelerating voltage, not the target material. So (A) is true. \(K_{\alpha}\) X-rays are characteristic X-rays, whose wavelengths are specific to the target material. So (R) is true. However, (R) explains characteristic X-rays, not the cut-off wavelength; thus, (R) is not a correct explanation for (A).
Assertion (A): In photoelectric effect, on increasing the intensity of light, both the number of electrons emitted and kinetic energy of each of them get increased but photoelectric current remains unchanged.
Reason (R): The photoelectric current depends only on wavelength of light.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Assertion (A) is false: Increasing intensity increases number of electrons and current, but KE remains same. Reason (R) is false: Photoelectric current depends on intensity and frequency. Both statements are false.
Assertion (A): Photons do not carry momentum
Reason (R): A photon is a material particle.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Assertion (A) is false: Photons carry momentum \(p = E/c = h/\lambda\). Reason (R) is false: A photon is a quantum of light/energy, not a classical material particle. Both statements are false.
Assertion (A): On the atomic scale, mass is measured in atomic mass units (u).
Reason (R): \(1u\) is \(1/12^{\text{th}}\) mass of one atom of \(C^{12}\) \(1u = 1.66 \times 10^{-27}\text{ kg}\).
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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Atomic mass unit (u) is a standard unit for expressing mass on an atomic scale. It is defined as exactly \(1/12^{\text{th}}\) the mass of an unbound neutral atom of carbon-12. This definition directly supports why (A) is true and explains the basis for its measurement.
Assertion (A): Bohr model can explain spectra of hydrogen or hydrogen like species.
Reason (R): Bohr model is the best atomic model.
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
Bohr's model successfully explains the spectra of hydrogen and hydrogen-like atoms. However, it fails for multi-electron atoms, cannot explain fine structure or the Zeeman effect, and is superseded by quantum mechanics. Therefore, it is not the best atomic model.
Assertion (A): Wavelength of continuous X-ray varies from a minimum value to infinity.
Reason (R): Continuous X-rays are emitted due to transition of electron from higher to lower energy level.
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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Continuous X-rays (Bremsstrahlung) are produced when high-speed electrons are decelerated in the electric field of atomic nuclei.
They have a continuous spectrum with a minimum wavelength. Characteristic X-rays, not continuous ones, are due to electron transitions between energy levels.
Assertion (A): Penetration power of hard X-ray is more than that of soft X-ray.
Reason (R): Hard X-ray is used for engineering purpose while soft X-ray is used for medical purpose.
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
Hard X-rays have shorter wavelengths and higher energy, leading to greater penetration power than soft X-rays. While both the assertion and reason are factually correct regarding X-ray properties and applications, the reason describes their uses, not the physical explanation for their differing penetration power.
Assertion (A): When white radiations (visible light) are passed through a sample of hydrogen gas at room temperature, absorption lines corresponding to Lyman series only are obtained.
Reason (R): At room temperature hydrogen atom is in the ground state.
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
At room temperature, hydrogen atoms are almost exclusively in their ground state (n=1). Therefore, absorption can only occur from \(n=1\) to higher energy levels (Lyman series). If 'white radiations' are assumed to include the necessary UV components, then only Lyman series absorption lines would appear, as other series require excited initial states.
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
View Answer
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.