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
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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 However, it fails for multi-electron atoms, cannot explain fine structure or the Zeeman effect, and is superseded by quantum mechanics.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
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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): An electron and a positron moving towards each other with equal and opposite velocities can annihilate into photons.
Reason (R): A photon has non zero energy and momentum.
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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Electron-positron annihilation converts their mass-energy into radiant energy, typically two gamma-ray photons to conserve momentum. Photons indeed possess non-zero energy and momentum. However, the reason describes a property of the resulting photons rather than the fundamental cause or mechanism of the annihilation process itself.
Assertion (A): For the scattering of \(\alpha\)-particles at a large angles only the nucleus of the atom is responsible.
Reason (R): Nucleus is very heavy in comparison to electrons.
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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In Rutherford's alpha-scattering experiment, large-angle deflections are caused by the strong electrostatic repulsion from the positively charged, massive nucleus. Electrons, being much lighter, cause negligible deflection. The nucleus's significant mass (R) ensures it remains largely stationary during collision, allowing for large deflections of \(\alpha\)-particles (A).
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
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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): 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.