Atomic Structure MCQ Quiz - Objective Question with Answer for Atomic Structure - Download Free PDF

Concept:

• Given Data
  • Atomic number of Be (Z) = 4
  • Orbit number (n) = 4
• The radius of the n-th orbit of a hydrogen-like ion is given by: \(r_n = \frac{n^2 \cdot a_0}{Z}\) , where:

\(r_n = \) radius of the n-th orbit
\(a_0\) = Bohr radius = 52.9 pm
Z = atomic number
n = orbit number

Calculation: 

• Substitute the given values into the formula:

\(r_4 = \frac{4^2 \cdot 52.9 \, \text{pm}}{4} \)

\(r_4 = \frac{16 \cdot 52.9 \, \text{pm}}{4}\)

\(r_4 = 4 \cdot 52.9 \, \text{pm}\)

\(r_4 = 211.6 \, \text{pm}\)

Conclusion:

The radius of the fourth orbit of\( \text{Be}^{3+}\) is:  211.6 pm

Calculation:

\(\text{Power}=60w\)

\(\text{Time} =10 \text{ hours}=10\times3600\text{ sec}=3.6\times10^4\text{ sec}\)

\(\text{Energy=power/times time}\)

\(\Rightarrow\text{Energy}=2.16\times10^6\text{ J}\)

\(E=\dfrac{hc}{\lambda}\)

given \(\lambda=6000A^0\)

Let n be the number of photons emitted

\(\Rightarrow\dfrac{12400}{6000}\times1.6\times10^{-19}\times n=60\times10\times60\times60\)

\(\Rightarrow n=6.5\times10^{24}\)

Hence, the correct option is (A)

CONCEPT:

Radial Nodes in Atomic Orbitals

• Radial nodes are regions where the probability of finding an electron is zero.
• The number of radial nodes in an atomic orbital is given by the formula:

  Number of radial nodes = n - l - 1

• Where:
  • n is the principal quantum number.
  • l is the azimuthal quantum number (for p-orbitals, l = 1).

EXPLANATION:

• For the 3p orbital:
  • The principal quantum number, n = 3.
  • The azimuthal quantum number for p-orbitals, l = 1.
• Using the formula for radial nodes:
  • Number of radial nodes = n - l - 1
  • = 3 - 1 - 1
  • = 1

Therefore, the number of radial nodes for the 3p orbital is 1.

CONCEPT:

Formation of Molecular Orbitals in Homonuclear Diatomic Molecules

• Molecular orbitals (MOs) are formed by the linear combination of atomic orbitals (AOs) when atoms combine.
• In homonuclear diatomic molecules, the internuclear axis is generally considered the z-axis.
• Conditions for effective molecular orbital formation:
  • Atomic orbitals must have compatible symmetry along the internuclear (z) axis.
  • Only orbitals aligned along the z-axis (like 2s, 2p_z, 3d_z²) can combine to form σ (sigma) molecular orbitals.
  • Orbitals perpendicular to the z-axis (such as 2p_x, 2p_y, or 3d_xy, 3d_x²−y²) do not form molecular orbitals due to lack of proper overlap.

EXPLANATION:

• Examining the given options:
  • A: 2p_z and 2p_x
    • 
      No molecular orbital formation because 2p_x is perpendicular to the z-axis.
  • B: 2s and 2p_x
    • 
      
    • No molecular orbital formation due to symmetry mismatch (2p_x is perpendicular to z-axis).
  • C: 3d_xy and 3d_x²−y²
    • 
      
      No molecular orbital formation because both d-orbitals lie in the xy-plane, not along the z-axis.
  • D: 2s and 2p_z
    • Molecular orbital formation occurs.
    • 
      
      Both orbitals align along the z-axis, leading to the formation of a σ molecular orbital.
  • E: 2p_x and 3d_x²−y²
    • 
      
    • No molecular orbital formation because both orbitals do not align along the z-axis.

Conclusion: Only option D (2s and 2p_z) leads to the formation of molecular orbitals in homonuclear diatomic molecules along the z-axis.

Hence, the correct answer is: Option 3 (D Only).

CONCEPT:

Rydberg Formula for Hydrogen Spectral Lines

• The Rydberg formula is used to determine the wavelength of light resulting from an electron moving between energy levels of a hydrogen atom.
• The formula is given by:

  \(\frac{1}{\lambda}=\mathrm{R}_{\mathrm{H}} \mathrm{Z}^{2} \times\left(\frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{2}^{2}}\right) \)

  where:

  • λ is the wavelength of the emitted photon
  • RH is the Rydberg constant
  • n1 and n2 are integers representing the initial and final energy levels (n2 > n1)

EXPLANATION:

λ = 900 nm \( \rm \quad\quad H-atom (Z = 1)\)

= 9 × 10–5 cm

RH = 105 cm–1 

Ryderg eq. = \(\frac{1}{\lambda}=\mathrm{R}_{\mathrm{H}} \mathrm{Z}^{2} \times\left(\frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{2}^{2}}\right) \)

⇒ \( \frac{1}{9 \times 10^{-5} \mathrm{~cm} \times 10^{5} \mathrm{~cm}^{-1}}=\left(\frac{1}{\mathrm{n}_{1}^{2}}-\frac{1}{\mathrm{n}_{2}^{2}}\right)\)

⇒ \( \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}=\frac{1}{9}\)

It is possible when n1 = 3, n2 = ∞ 

Possible series : ∞ → 3

Therefore, the spectral line of the H atom suitable for 900 nm radiation is Paschen series, 5 → 3

Explanation:

John Dalton Postulates about atoms.

• All matter is made up of tiny, indivisible particles called atoms.
• All atoms of a specific element are identical in mass, size, and other properties. However, atoms of different element exhibit different properties and vary in mass and size.
• Atoms can neither be created nor destroyed. Furthermore, atoms cannot be divided into smaller particles.
• Atoms of different elements can combine with each other in fixed whole-number ratios in order to form compounds.
• Atoms can be rearranged, combined, or separated in chemical reactions

Important Points

John Dalton raised the atomic theory that acted as an explanation of the following two laws. 

• Law of conservation of mass:
  • According to the law, mass can neither be destroyed nor created in any chemical reaction.
• Law of constant proportion/ definite proportion:
  • The laws state that in a chemical substance, the elements are always present in certain proportions by mass.
• For example:
  • Oxygen & Hydrogen are present in water in a ratio of 8:1.
  • So we will obtain 1g of hydrogen and 8g of oxygen if we decompose 9g of water.
• Atom: 
  • An atom is the smallest invisible unit of matter that constitutes a chemical element.
  • Every plasma, solid, gas & liquid, composed of ionized or neutral atoms.
  • Around 100 picometers across, atoms are extremely small. 
• Atomic theory: 
  • John Dalton discovered atomic theory.
  • As per the theory, all matter whether it is a mixture, compound, element, is consists of invisible particles called ‘atoms’. 

Explanation:

• Isotopes are atoms of the same element that have different numbers of neutrons but the same number of protons and electrons.
• The difference in the number of neutrons between the various isotopes of an element means that the various isotopes have different masses.

So, The difference in isotopes of an element is the mass number.Additional Information 

The correct answer is Both I and II.

Key Points

• I. The atomic number of an element is indeed equal to the number of protons in an atom of that element.

Hence correct.

• II. The mass number of an atom is defined as the total number of protons and neutrons (collectively known as nucleons) in an atom.

Hence correct.

Additional Information

• In this example, Carbon has an atomic number of 6, which means it has 6 protons in the nucleus of each of its atoms.
  • This atomic number defines the element
  • In other words, any atom with 6 protons is a Carbon atom.
  • The mass number of Carbon is 12, indicating that the total number of protons and neutrons in the nucleus is 12.
    • Since we know there are 6 protons (from the atomic number), this means there must also be 6 neutrons (because 12 total nucleons - 6 protons = 6 neutrons).
• The atomic number and mass number are crucial in defining an atom's identity and properties.
  • The atomic number determines the element and its place in the periodic table, while the mass number helps to identify isotopes (varieties of the same element with different numbers of neutrons).

The correct answer is isobars.

Key Points

• The nuclei have been classified based on the number of protons (atomic number) of the total number of nucleons (mass number) as follows -
• Isotopes: The atoms of an element having the same atomic number but a different mass number are called isotopes.
• All isotopes have the same chemical properties.
• Isobars: The nuclei which have the same mass number (A) but a different atomic number (Z) are called isobars.
• Isotones: The nuclei having an equal number of neutrons are called isotones. For them both the atomic number (Z) and mass number (A) are different, but the value of (A – Z) is the same.

Explanation:

• From above it is clear that the nuclei which have the same mass number (A) but a different atomic number (Z) are called isobars. Therefore option 3 is correct.
• Isobars occupy different positions in the periodic table so all isobars have different chemical properties.

Example of Isobars:

Explanation:

John Dalton Postulates about atoms.

• All matter is made up of tiny, indivisible particles called atoms.
• All atoms of a specific element are identical in mass, size, and other properties. However, atoms of different element exhibit different properties and vary in mass and size.
• Atoms can neither be created nor destroyed. Furthermore, atoms cannot be divided into smaller particles.
• Atoms of different elements can combine with each other in fixed whole-number ratios in order to form compounds.
• Atoms can be rearranged, combined, or separated in chemical reactions

Important Points

John Dalton raised the atomic theory that acted as an explanation of the following two laws. 

• Law of conservation of mass –
  • According to the law, mass can neither be destroyed nor created in any chemical reaction.
• Law of constant proportion/ definite proportion –
  • The laws state that in a chemical substance, the elements are always present in certain proportions by mass.
• For example:
  • Oxygen & Hydrogen are present in water in a ratio of 8:1.
  • So we will obtain 1g of hydrogen and 8g of oxygen if we decompose 9g of water.
• Atom: 
  • An atom is the smallest invisible unit of matter that constitutes a chemical element.
  • Every plasma, solid, gas & liquid, composed of ionized or neutral atoms.
  • Around 100 picometers across, atoms are extremely small. 
• Atomic theory: 
  • John Dalton discovered atomic theory.
  • As per the theory, all matter whether it is a mixture, compound, element, is consists of invisible particles called ‘atoms’. 

The correct answer is Tetra-atomic.

Key Points

• Phosphorus is represented by P4.
• The number of atoms present in a phosphorus molecule is 4.
• Therefore, the atomic number of phosphorus is 4 because it is atom four.

Important Points

• The number of atoms that make up a molecule is called its atomic number.
• Atomicity is monatomic if there is only one atom, diatomic if there are two atoms, triatomic if there are three atoms, and so on.
• If there are more than four atoms, atomicity is polyatomic.

Additional Information

• Mono-atomic:
  • Monoatomic or monad elements are elements that are stable as single atoms.
  • Mon- or Mono- means one. For an element to stabilize itself, it must have a stable set of eight valence electrons.
• Poly-atomic:
  • if an ion consists of two or more atoms, it can be called a polyatomic ion or molecular ion.
• Di-atomic:
  • A molecule of a detail that has atomicity 2 or has 2 atoms in its molecule, is referred to as a diatomic.
  • example:- hydrogen, oxygen, and nitrogen are diatomic.

Concept:

• The Aufbau principle rationalization of the distribution of electrons among energy levels in the ground (most stable) states of atoms.
• It is a German word which means "to build up".
• The principle formulated by the Danish physicist Niels Bohr about 1920.

Explanation:

The greater is the value of (n+l), the greater is the energy of orbitals.

(a) n = 4, l = 1 ⇒ 4p orbital

(b) n = 4, l = 0 ⇒ 4s orbital

(c) n = 3, l = 2 ⇒ 3d orbital

(d) n = 3, l = 1 ⇒3p orbital

According to the Aufbau principle, energies of above-mentioned orbitals are in the order of-

The increasing order of energy (d) 3p < (b) 4s < (c) 3d < (a) 4p

So, (d) < (b) < (c) < (a) is correct order.

Concept:

Heisenberg’s Uncertainty Principle:

• W Heisenberg a German physicist in 1927, stated the uncertainty principle which is the consequence of dual behavior of matter and radiation.
• It states that it is impossible to determine simultaneously, the exact position and exact momentum (or velocity) of an electron.

According to Heisenberg’s Uncertainty Principle

\({\rm{Δ }}x \times {\rm{Δ }}P\; \ge \frac{h}{{4\;\pi \;}}\)

Where, Δx = Uncertainty in position, ΔP = Uncertainty in momentum, h = Plank’s constant

ΔP = m Δv

Where, ΔP = Uncertainty in momentum, m = mass of particle, Δv = Uncertainty in velocity.
Calculation:

Given: Δx = m Δv

According to Heisenberg’s Uncertainty Principle

\({\rm{Δ }}x \times {\rm{Δ }}P\; \ge \frac{h}{{4\;\pi \;}}\)

ΔP = m Δv

\({\rm{Δ }}x \times {\rm{mΔ }}v\; \ge \frac{h}{{4\;\pi \;}}\)

\({\rm{mΔ }}v \times {\rm{mΔ }}v\; \ge \frac{h}{{4\;\pi \;}}\)

\({m^2}{\rm{\Delta }}{v2} = \frac{h}{{4\pi }}\)

\({\rm{\Delta }}v = \sqrt {\frac{h}{{4\pi }}} \times \frac{1}{m}\)

\(\Delta v =\frac{1}{{2\;m}}\sqrt {\frac{h}{\pi }} \)

The correct answer is Protons and Neutrons.

Key Points

• In every atom Electron, Proton and Neutrons are present.

​The correct answer is Only I and II.

Important PointsJohn Dalton Postulates about atoms.

• All matter is made up of tiny, indivisible particles called atoms.
• All atoms of a specific element are identical in mass, size, and other properties. However, atoms of different elements exhibit different properties and vary in mass and size.
• Atoms can neither be created nor destroyed. Furthermore, atoms cannot be divided into smaller particles.
• Atoms of different elements can combine with each other in fixed whole-number ratios in order to form compounds.
• Atoms can be rearranged, combined, or separated in chemical reactions

 Key Points

• Atomic theory by Dalton:-
  • It proposed that all matter is composed of very tiny particles who he named ‘atoms’ and they consist of non-destructible and indivisible building blocks.
  • Dalton's atomic theory also proposed that all atoms of an element are identical in nature and different elements vary in size, mass and chemical properties. So, the correct answer is option 1 which says that first and second statements are correct.