Structure of atom practice · Mixed difficulty

Option D ($4.42 \times {10^{ - 18}}$) is correct because it is calculated using the formula $E = \frac{{hc}}{\lambda }$ with correct unit conversions.

Option A is correct because the statement is correct (number of subshells = shell number), but the explanation is wrong as Sommerfeld's model explains elliptical orbits, not the number of subshells.

Option D ($2.12\,\mathop \mathrm{A}\limits^ \circ$) is correct because it is calculated using the formula for the radius of the nth Bohr orbit for hydrogen atom.

Option A (Atoms can be created in a chemical reaction) is correct because Dalton's atomic theory states that atoms are indivisible and cannot be created or destroyed in a chemical reaction.

Option D (Characteristics of cathode rays depend upon the nature of gas present in the cathode ray tube) is correct because the characteristics of cathode rays do not depend on the gas present in the tube.

Option A ([Xe] 4f14 5d9 6s1) is correct because Platinum (Pt) has an atomic number of 78, and its electronic configuration follows Hund's rule and the Aufbau principle, with one electron promoted from the 5d to the 6s orbital for stability.

Option D (3s) is correct because s-orbitals are spherically symmetrical and therefore non-directional.

Option C (Zeeman effect) is correct because the splitting of spectral lines in a magnetic field is known as the Zeeman effect.

Option D (Any of these) is correct because for a given azimuthal quantum number $l$, the principal quantum number $n$ must be greater than or equal to $l+1$.

Option D (iii)<(iv)<(i)<(ii) is correct because electron affinity increases across a period and decreases down a group, with exceptions due to small size.

Option B ($1.46 \times 10^{-33} \mathrm{~m}$) is correct because it is the uncertainty in position calculated using Heisenberg's uncertainty principle.

Option C ($\sqrt{\frac{\lambda R}{\lambda R-1}}$) is correct because it is the quantum number derived from the Rydberg formula for the given transition.

Option D is correct because $V^{2+}$ has unpaired d-electrons, allowing for d-d transitions and thus exhibiting color.

Option B ($1.6 \times {10^{ - 12}}\mathrm{erg}$) is correct because 1 eV is equal to $1.602 \times 10^{-19}$ J, which is equivalent to $1.602 \times 10^{-12}$ erg.

The correct answer is C (Both S and E are correct and E is correct explanation of S) because the probability density at the nucleus is non-zero for s-orbitals, and the given equation correctly describes the dependence of the wave function on the distance from the nucleus.

Option B (Paschen series) is correct because the Paschen series corresponds to transitions where electrons fall to the n=3 energy level.

Option A ($l$) is correct because the orbital angular momentum depends only on the azimuthal quantum number ($l$).

Option C (Nucleus) is correct because Rutherford's alpha-particle scattering experiment demonstrated the existence of a small, dense, positively charged nucleus within the atom.

Option B ($6.63 \times 10^{-29} \mathrm{~m}$) is correct because it is calculated by substituting the given values into the de Broglie wavelength formula.

Option D (4 × 10¹⁹) is correct because it is calculated using the formula p = (n*hc)/(t*lambda) and considering the efficiency of the bulb.

Option C (0.5) is correct because the quantum efficiency is calculated by dividing the moles of B formed by the moles of photons absorbed.

Option B (1 proton, 1 neutron) is correct because a deuterium nucleus is an isotope of hydrogen with one proton and one neutron.

Option A ($1.14 \times 10^{-6} \mathrm{~m}$) is correct because the wavelength is calculated using the Rydberg formula with the correct values for n1, n2, and Z.

Option B (Zeernan effect, stark effect) is correct because the splitting of spectral lines in a magnetic field is called the Zeeman effect, while the splitting in an electric field is called the Stark effect.

Option C (Both (1) and (2)) is correct because both the dual character of electromagnetic radiation and experimental results regarding atomic spectra were responsible for Bohr's model.

Option A ($M{n^{ + 2}}$) is correct because it has the maximum number of unpaired electrons (5), leading to the highest magnetic moment.

Option B ($\mathrm{F}{\mathrm{e}^{2 + }}$) is correct because it has the most unpaired electrons (4) in its d-orbital configuration.

The correct answer is A (0.1 kg) because the mass is calculated using the de Broglie wavelength formula.

Option B (Less than electron) is correct because protons are much more massive than electrons, and therefore have lower penetration power.

Option A (662) is correct because it is the result of applying the formula relating energy and wavelength of a photon.