JEE Chemistry Structure of the Atom MCQs Set 10

Answer: (d) 12.75 V

Explanation:
1. The first Paschen line is the transition 4 to 3, so the atom must first be excited to n = 4.
2. Excitation from n = 1 to n = 4 needs \(13.6\left(1 - \frac1{16}\right) = 12.75\) eV.
3. So electrons accelerated through 12.75 V are needed.

Teacher's Note:
1. The atom must reach the n = 4 level before it can emit the 4 to 3 line.
2. Accelerating potential in volts equals the energy in eV.

Answer: (d) 54.4, 13.6, 6

Explanation:
1. For \(\ce{He+}\), \(E_n = -\frac{54.4}{n^2}\) eV.
2. n = 1: 54.4 eV; n = 2: 13.6 eV; n = 3: 6.04 eV.
3. So the energies are 54.4, 13.6 and about 6 eV.

Teacher's Note:
1. Multiply the hydrogen values by \(Z^2 = 4\).
2. Binding energy is the magnitude of the level energy.

Answer: (a) \(n_3 \to n_2\)

Explanation:
1. Energy gaps in units of 13.6 eV: 3 to 2 = 0.139, 4 to 3 = 0.049, 5 to 4 = 0.0225.
2. The largest gap is for 3 to 2.

Teacher's Note:
1. Gaps between adjacent levels shrink as n increases.
2. The lowest adjacent pair gives the largest energy.

Answer: (c) 10 Å

Explanation:
1. For hydrogen-like ions, \(\lambda \propto \frac{1}{Z^2}\) for the same transition.
2. \(\lambda = \frac{1216}{11^2} = \frac{1216}{121} = 10.05\) Å.
3. So about 10 Å.

Teacher's Note:
1. \(\ce{Na^{10+}}\) has one electron and Z = 11.
2. Larger Z shifts lines to much shorter wavelengths.

Answer: (c) 3

Explanation:
1. Four ultraviolet (Lyman) lines mean the electron started at n = 5 (5 to 1, 4 to 1, 3 to 1, 2 to 1).
2. The other lines from n = 5: 5 to 2, 4 to 2 and 3 to 2 (visible), and 5 to 4, 5 to 3 and 4 to 3 (infrared).
3. So 3 infrared lines.

Teacher's Note:
1. List all pairs among the five levels (10 lines in total).
2. Lines ending at n = 3 or 4 fall in the infrared.

Answer: (b) \(\ell = \frac{m - 1}{2}\)

Explanation:
1. The number of m values (orbitals) for a given \(\ell\) is \(m = 2\ell + 1\).
2. Solving, \(\ell = \frac{m - 1}{2}\).

Teacher's Note:
1. Here m on the right-hand side means the number of values.
2. Check: \(\ell\) = 2 gives m = 5.

Answer: (a) \(\ell\) = 0, m = 0; \(\ell\) = 1, m = +1, 0, -1; \(\ell\) = 2, m = +2, +1, 0, -1, -2

Explanation:
1. For n = 3, \(\ell\) = 0, 1, 2.
2. For each \(\ell\), m ranges from -\(\ell\) to +\(\ell\) in integer steps: 0; +1, 0, -1; +2, +1, 0, -1, -2.
3. Only option (a) lists these correctly.

Teacher's Note:
1. \(\ell\) goes from 0 to n - 1.
2. m has \(2\ell + 1\) values.

Answer: (a) kernel

Explanation:
1. The nucleus together with all the inner (non-valence) electrons is called the kernel.
2. The term "kernel" is used for the atom without its outer shell.

Teacher's Note:
1. The kernel carries a net positive charge equal to the number of valence electrons.
2. It is also described as the atomic core in some texts.

Answer: (a) n = 2

Explanation:
1. \(r \propto n^2\).
2. \(n^2 = \frac{21.2 \times 10^{-11}}{5.3 \times 10^{-11}} = 4\).
3. So n = 2.

Teacher's Note:
1. The ground-state radius corresponds to n = 1.
2. Take the square root of the ratio.

Answer: (d) Both Assertion and Reason are false.

Explanation:
1. Mass numbers are always whole numbers (the count of protons plus neutrons).
2. It is the atomic masses that are often fractional, because of the mixture of isotopes.
3. The reason is also incorrect as stated, since mass numbers are counts and not comparisons, so both are false.

Teacher's Note:
1. Mass number is a whole number and atomic mass is an average.
2. The C-12 scale is used to define atomic masses.

Answer: (c) Assertion is true but the Reason is false.

Explanation:
1. \(v \propto \frac{Z}{n}\), so the velocity decreases as n increases, and the assertion is true.
2. \(r \propto n^2\), so \(v \propto \frac{1}{\sqrt r}\), which is not inversely proportional to r, so the reason is false.

Teacher's Note:
1. Velocity falls as 1/n while radius rises as \(n^2\).
2. Only the product of v and r is inversely related to the mass.

Answer: (a) Both Assertion and Reason are true and the Reason is a correct explanation of the Assertion.

Explanation:
1. The energy of a bound electron is lower than that of a free electron at rest at infinity, which is taken as zero, so it is negative.
2. Both statements are true, and the bound state is the reason for the negative energy.

Teacher's Note:
1. Negative energy means the electron is attracted to the nucleus.
2. A positive total energy would mean a free electron.

Answer: (a) Both Assertion and Reason are true and the Reason is a correct explanation of the Assertion.

Explanation:
1. Bohr's model works for one-electron species only.
2. It has no provision for the repulsion between electrons, which is exactly why it fails for multi-electron atoms.
3. Both are true and the reason explains the assertion.

Teacher's Note:
1. Electron-electron repulsion makes multi-electron atoms much more complex.
2. Bohr's quantisation does not handle it.

Answer: (b) Both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion.

Explanation:
1. A p orbital is indeed dumbbell shaped (true).
2. The three m values 0, +1, -1 belong to the three p orbitals of a subshell, which is also true.
3. But m describes the orientation of the orbital and not its shape, so the reason does not explain the assertion.

Teacher's Note:
1. The shape depends on \(\ell\) and the orientation on m.
2. Both statements are true but unrelated as cause and effect.

Answer: (a) Both Assertion and Reason are true and the Reason is a correct explanation of the Assertion.

Explanation:
1. A nodal plane is a plane where the electron density is zero.
2. The p\(_x\) orbital lies along the x-axis and has zero density in the yz plane.
3. The reason is simply the definition of the nodal plane, so it explains the assertion.

Teacher's Note:
1. A p orbital has one nodal plane, perpendicular to its axis.
2. The p\(_x\) orbital's axis is x, so the nodal plane is yz.

Answer: (a) Both Assertion and Reason are true and the Reason is a correct explanation of the Assertion.

Explanation:
1. Spherical (radial) nodes = n - \(\ell\) - 1. For \(\ell\) = 1 this is n - 2.
2. For 2p, n - 2 = 0, so there are no spherical nodes.
3. The reason gives exactly this formula, so it explains the assertion.

Teacher's Note:
1. Radial nodes = n - \(\ell\) - 1.
2. 3p has one radial node and 2p has none.

Answer: (b) Both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion.

Explanation:
1. Radial nodes = n - \(\ell\) - 1 = 3 - 0 - 1 = 2, so the assertion is true.
2. Angular nodes = \(\ell\) = 0, so the reason is also true.
3. The absence of angular nodes does not explain the number of spherical nodes, so it is not the correct explanation.

Teacher's Note:
1. Radial and angular nodes are counted separately.
2. Total nodes = n - 1.

Answer: (c) Assertion is true but the Reason is false.

Explanation:
1. For 3p: radial nodes = 3 - 1 - 1 = 1 and angular nodes = \(\ell\) = 1, so the assertion is true.
2. The numbers of nodes depend on both n and \(\ell\), not on n alone, so the reason is false.

Teacher's Note:
1. Radial nodes need n and \(\ell\); angular nodes equal \(\ell\).
2. Total nodes depend only on n (n - 1).

Answer: (c) Assertion is true but the Reason is false.

Explanation:
1. In hydrogen (one electron) the energy depends only on n, so the assertion is true.
2. In multi-electron atoms the energies of s, p, d and f of the same n are different, so the reason, stated for any atom, is false.

Teacher's Note:
1. Degeneracy within a shell holds only for one-electron species.
2. Electron repulsion splits the subshells in other atoms.

Answer: (b) Both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion.

Explanation:
1. The assertion is a consequence of the Pauli exclusion principle, so it is true.
2. Opposite spins do create opposite magnetic fields, which is also true.
3. But the limit of two electrons arises from Pauli's principle, not from the magnetic fields, so the reason does not explain it.

Teacher's Note:
1. Opposite spins make the two electrons different in the fourth quantum number.
2. A third electron would have to repeat a spin value.

Answer: (b) Both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion.

Explanation:
1. In hydrogen the energy depends only on n, so 4s (n = 4) is above 3d (n = 3), and the assertion is true.
2. The (n + \(\ell\)) rule is a true rule for multi-electron atoms.
3. But it would predict 4s (4) below 3d (5), so it does not explain the hydrogen result.

Teacher's Note:
1. The (n + \(\ell\)) rule applies only to multi-electron atoms.
2. In hydrogen only n matters.

Answer: (b) Both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion.

Explanation:
1. An s orbital holds at most 2 electrons, so 2s3 is impossible, and the assertion is true.
2. Hund's rule does demand maximum multiplicity, so the reason is true.
3. But the prohibition on 2s3 comes from Pauli's exclusion principle, not from Hund's rule.

Teacher's Note:
1. Boron is 1s2 2s2 2p1.
2. Pauli's principle limits each orbital to two electrons.

Answer: (a) Both Assertion and Reason are true and the Reason is a correct explanation of the Assertion.

Explanation:
1. Cr is [Ar] 3d5 4s1 rather than 3d4 4s2, so the assertion is true.
2. The extra stability of a half-filled d subshell (greater exchange energy) is the reason for moving one 4s electron into 3d.
3. The reason explains the assertion.

Teacher's Note:
1. Half-filled and fully filled subshells are specially stable.
2. Cu (3d10 4s1) is another example.

Answer: (b) Both Assertion and Reason are true but the Reason is not a correct explanation of the Assertion.

Explanation:
1. A colliding electron can give up part of its energy, so 10.2 eV can be absorbed (n = 1 to 2) and the electron keeps the remaining 0.4 eV, so the assertion is true.
2. The gap between n = 1 and n = 2 is 10.2 eV, so the reason is also true.
3. The reason states only the gap, not why a beam of larger energy can excite, so it is not a complete explanation.

Teacher's Note:
1. An electron beam can transfer a fraction of its energy, unlike a photon.
2. The gap is a fact about the atom.

Answer: (a) Both Assertion and Reason are true and the Reason is a correct explanation of the Assertion.

Explanation:
1. A neutral He atom has two electrons, and Bohr's model works only for one-electron species.
2. Bohr's theory ignores electron-electron repulsion, which is exactly why it fails for He.
3. So the reason explains the assertion.

Teacher's Note:
1. \(\ce{He+}\) (one electron) can be handled by Bohr's model but He cannot.
2. The repulsion term is missing in Bohr's theory.