Discovery of neutron


James Chadwick discovered the neutron in 1932 by bombarding beryllium with alpha particles, which emitted radiation unaffected by electric or magnetic fields, suggesting it carried no charge. Neutrons, slightly heavier than protons, play a crucial role in stabilizing atomic nuclei, especially in isotopes, where the number of neutrons varies but protons remain constant. This discovery helped explain isotopes' existence.

Numerical Example:

- Calculate the number of protons, neutrons, and electrons in \(_{26}^{56}Fe\). 

  Solution: 

  Protons = 26, Neutrons = \( 56 - 26 = 30 \), Electrons = 26 (neutral atom).

 

Questions

Q 1. The discovery of neutron became very late because :;

(d) all of the above;

(c) neutrons are fundamental particles;

(b) neutrons are chargeless;

(a) neutrons are present in nucleus;

Q 2. Neutron is discovered by;

(d) Dalton;

(c) Yukawa;

(b) Rutherford;

(a) Chadwick;

Q 3. Which of the following properties of atom could be explained correctly by Thomson Model of atom?;

(d) Stability of atom.;

(c) Position of electrons, protons and neutrons in atom.;

(b) Spectra of hydrogen atom.;

(a) Overall neutrality of atom.;

Q 4. Arrange the following in terms of penetrating power \(\alpha)-rays, \(\beta\)-rays, \(\gamma\)-rays;

(b) \(\alpha > \gamma > \beta \);

(c) \(\alpha > \beta < \gamma\);

(b) \(\alpha < \beta < \gamma\);

(a) \(\alpha > \beta > \gamma\);

Q 5. Which of the rays are not deflected by the electric and magnetic field?;

(d) Both (a) and (b);

(c) \(\beta)rays;

(b) X-rays;

(a) \(\gamma\)-rays;

Q 6. Rutherford's experiment on the scattering of \(\alpha\(-particles showed for the first time that the atom has :;

(a) electrons;

(b) protons;

(c) nucleus;

(d) neutrons';

Q 7. Rutherford's experiment which established the nuclear model of the atom used a beam of;

(a) \(\beta\(-particles which impinged on a metal foil and got absorbed ;

(b) \(\gamma\(-rays which impinged on a metal foil and ejected electrons;

(c) helium atoms, which impinged on a metal foil and got scattered;

(d) helium nuclei, which impinged on a metal foil and got scattered;

Q 8. Which of the following scientists explained his model on the basis of centrifugal force?;

(a) Thomson;

(b) Dalton;

(c) Millikan;

(d) Rutherford;

Q 9. The number of neutrons in dipositive zinc ion with mass number 70 is;

(a) 34;

(b) 36;

(c) 38;

(d) 40;

Q 10. Millikan performed an experiment method to determine which of the following?;

(d) Both (a) and (b);

(c) \(\mathrm{e} / \mathrm{m}\( ratio of electron;

(b) Charge of the electron;

(a) Mass of the electron;

Proton characteristics


Protons are positively charged particles found in the nucleus, with a charge of \( +1e \) and a mass of \( 1.672 \times 10^{-27} \) kg. Ernest Rutherford discovered the proton during his gold foil experiment in 1917. Protons determine the atomic number (Z) of an element and, along with neutrons, contribute to the atomic mass.

 

Numerical Example:

- Determine the number of protons, neutrons, and electrons in \(_{17}^{35}Cl^-\). 

  Solution: 

  Protons = 17, Neutrons = \( 35 - 17 = 18 \), Electrons = \( 17 + 1 = 18 \) (due to the negative charge).

 

Questions

Q 1. Which is correct statement about proton?;

(a) Proton is nucleus of deuterium;

(b) Proton is \(\alpha\(-particle;

(c) Proton is ionized hydrogen molecule;

(d) Proton is ionized hydrogen atom;

Pauli exclusion principle


The Pauli Exclusion Principle, introduced in 1926, asserts that no two electrons in an atom can share the same set of quantum numbers. This limits each orbital to two electrons with opposite spins. The principle is vital for understanding electronic configurations, the periodic table, and the structure of atoms.

 

Numerical Example:

- Assign quantum numbers for the two electrons in the 2s orbital of a helium atom. 

  Solution: 

  First electron: \( n = 2, l = 0, m_l = 0, m_s = +\frac{1}{2} \). 

  Second electron: \( n = 2, l = 0, m_l = 0, m_s = -\frac{1}{2} \).

 

Questions

Q 1. The lightest particle is :;

(a) \(\alpha\)-particle;

(b) positron;

(c) proton;

(d) neutron;

Q 2. Nucleons are;

(a) only neutrons;

(b) neutrons + protons;

(c) neutrons + protons + electrons;

(d) neutrons + electrons;

Q 3. Which one is a wrong statement? [2018];

(a) Total orbital angular momentum of electron in ' \(s\) ' orbital is equal to zero;

(b) An orbital is designated by three quantum numbers while an electron in an atom is designated by four quantum numbers;

(c) The value of \(m\) for \(d_{z}^{2}\) is zero;

(d) The electronic configuration of \(\mathrm{N}\) atom is;

Q 4. Which one is the wrong statement? [2017];

(a) The uncertainty principle is \(\Delta E \times \Delta t \geq h / 4 \pi\);

(b) Half filled and fully filled orbitals have greater stability due to greater exchange energy, greater symmetry and more balanced arrangement.;

(c) The energy of 2 sorbital is less than the energy of \(2 p\) orbital in case of Hydrogen like atoms;

(d) de-Broglie's wavelength is given by \(\lambda=\frac{h}{m v}\), where \(m=\) mass of the particle, \(v=\) group velocity of the particle;

Structure of subatomic particles


Atoms consist of three primary subatomic particles: protons, neutrons, and electrons. Protons and neutrons are located in the nucleus, while electrons orbit the nucleus in designated energy levels. Protons have a positive charge, neutrons are neutral, and electrons carry a negative charge. The relative masses and charges of these particles govern atomic structure and behavior.

 

Numerical Example:

- For \(_{15}^{31}P\), calculate the number of protons, neutrons, and electrons. 

  Solution: 

  Protons = 15, Neutrons = \( 31 - 15 = 16 \), Electrons = 15.

 

Questions

Q 1. When beryllium is bombarded with alpha particles (Chadwick's experiment) extremely penetrating radiations, which cannot be deflected by electrical or magnetic field are given out These are :;

(a) A beam of protons;

(b) Alpha rays;

(c) A beam of neutrons;

(d) A beam of neutrons and protons;

Q 2. Suppose beam containing all three fundamental subatomic particles are allowed to pass through an electric field as shown in figure The subatomic particles detected at three points \(\mathrm{A}, \mathrm{B}\( and \(\mathrm{C}\( on the screen respectively are ?;

(a) Protons, neutrons, electrons;

(b) Electrons, neutrons, protons;

(c) Electrons, protons, neutrons;

(d) Neutrons, protons, electrons;

Q 3. When atoms are bombarded with alpha particles, only, a few in million suffer deflection, others pass out undeflected This is because;

(a) the force of repulsion on the moving alpha particle is small;

(b) the force of attraction between alpha particle and oppositely charged electrons is very small;

(c) there is only one nucleus and large number of electrons;

(d) the nucleus occupies much smaller volume compared to the volume of the atom;

Q 4. If the alpha-particles are projected against the following atoms \(\mathrm{Fe}, \mathrm{Be}, \mathrm{Mg}, \mathrm{Al}\) then increasing order in which the alpha-particle feel repulsion will be;

(a) \(\mathrm{Be}, \mathrm{Mg}, \mathrm{Al}, \mathrm{Fe}\);

(b) \(\mathrm{Be}, \mathrm{Al}, \mathrm{Mg}, \mathrm{Fe}\);

(c) \(\mathrm{Mg}, \mathrm{Al}, \mathrm{Mg}, \mathrm{Fe}\);

(d) \(\mathrm{Al}, \mathrm{Mg}, \mathrm{Fe}, \mathrm{Be}\);

Rutherford's nuclear model


In 1911, Ernest Rutherford proposed the nuclear model of the atom based on his gold foil experiment. He demonstrated that atoms consist of a small, dense, positively charged nucleus surrounded by electrons in orbits. Most of the atom's mass is concentrated in the nucleus, with electrons occupying most of the atom's volume.

 

Numerical Example:

- If alpha particles are scattered by a gold foil, calculate the percentage of particles that pass through undeflected, given most of the atom is empty space. 

  Solution: 

  Approximately 99% pass through undeflected due to the atom’s empty space.

 

Questions

Q 1. Rutherford's \(\alpha\(-particle dispersion experiment concludes;

(a) all positive ions are deposited at small part;

(b) all negative ions are deposited at small part;

(c) proton moves around the electron;

(d) neutrons are charged particles.;

Q 2. Bohr model can explain :;

(a) the solar spectrum;

(b) the spectrum of hydrogen molecule;

(c) spectrum of any atom or ion containing one electron only;

(d) the spectrum of hydrogen atom only;

de Broglie relation


Louis de Broglie’s hypothesis in 1924 proposed that particles exhibit wave-like behavior. The de Broglie wavelength \( \lambda \) is given by \( \lambda = \frac{h}{p} \), where \( h \) is Planck’s constant and \( p \) is the momentum of the particle. This relation is fundamental in quantum mechanics and explains phenomena such as electron diffraction.

 

Numerical Example:

- Calculate the de Broglie wavelength of an electron traveling at \( 2 \times 10^6 \) m/s. 

  Solution: 

  \( \lambda = \frac{6.626 \times 10^{-34}}{9.1 \times 10^{-31} \times 2 \times 10^6} = 3.64 \times 10^{-10} \) m.

 

Relevant Image: Use wave-particle duality equations from NCERT.

Questions

Q 1. Which is not true with respect to cathode rays?;

(a) A stream of electrons;

(b) Charged particles;

(c) Move with speed same as that of light;

(d) Can be deflected by magnetic fields;

Q 2. Cathode rays are deflected by;

(a) an electric field only;

(b) magnetic field only;

(c) by both;

(d) by none;

Q 3. The orbitals are called degenerate when;

(a) they have the same wave functions;

(b) they have the same wave functions but different energies;

(c) they have different wave functions but same energy;

(d) they have the same energy;

Q 4. The orbitals are called degenerate when [1996];

(a) they have the same wave functions;

(b) they have the same wave functions but different energies;

(c) they have different wave functions but same energy;

(d) they have the same energy;

Thomson's model of atom


In 1898, J.J. Thomson proposed that atoms consist of a positively charged “pudding” with negatively charged electrons embedded like “plums.” This model explained atomic neutrality but was later disproved by Rutherford’s gold foil experiment, which showed that positive charge is concentrated in a nucleus.

 

Numerical Example:

- Why did Thomson's model fail? 

  Solution: 

  Thomson's model couldn’t explain the deflection of alpha particles in Rutherford’s experiment.

 

Questions

Q 1. Two atoms are said to be isotopes if:;

(D) They have same number of neutrons but different modes of radioactive decay;

(C) The sum of the number of protons and neutrons is same but number of protons are different;

(B) They have same number of neutrons but different mass number;

(A) They have same atomic number but different mass numbers;

Q 2. Two atoms are said to be isotopes if:;

(D) They have same number of neutrons but different modes of radioactive decay;

(C) The sum of the number of protons and neutrons is same but number of protons are different;

(B) They have same number of neutrons but different mass number;

(A) They have same atomic number but different mass numbers;

Q 3. The Bohr orbit radius for the hydrogen atom \((n=1)\) is approximately \(0 530 \AA\) The radius for the first excited state (n=2) orbit is (in \(\AA\) );

(d) 2.12;

(c) 4.77;

(b) 1.06;

(a) 0.13;

Q 4. The Bohr orbit radius for the hydrogen atom \((n=1)\) is approximately \(0.530 \ \text{\AA}\). The radius for the first excited state \((n=2)\) orbit is (in \(\text{\AA}\)): [1998];

(a) 0.13;

(b) 1.06;

(c) 4.77;

(d) 2.12;

Q 5. If ionization potential for hydrogen atom is \(13 6 \mathrm{eV}\), then ionization potential for \(\mathrm{He}^{+}\)will be;

(a) \(54.4 \mathrm{eV}\);

(b) \(6.8 \mathrm{eV}\);

(c) \(13.6 \mathrm{eV}\);

(d) \(24.5 \mathrm{eV}\);

Discovery of electron


J.J. Thomson discovered the electron in 1897 through experiments with cathode rays. He showed that cathode rays were made of negatively charged particles (electrons). His discovery laid the foundation for modern atomic theory, revealing that atoms are divisible and consist of smaller charged particles.

 

Numerical Example:

- In a cathode ray tube, calculate the charge-to-mass ratio of an electron if the applied electric field is \( 1.0 \times 10^4 \) V/m and the electron is deflected by \( 5 \times 10^{-4} \) m. 

  Solution: 

  Use \( e/m = 1.76 \times 10^{11} \, \text{C/kg} \).

 

Questions

Q 1. In photoelectric effect, at which frequency electron will be ejected with certain kinetic energy ( \(v_{0}=\) threshold frequency);

(d) \(v \geq v_{0}\);

(c) \(v_{0} \geq v\);

(b) \(v_{0}>v\);

(a) \(v>v_{0}\);

Q 2. An electron from one Bohr stationary orbit can go to next higher orbit;

(d) without emission or absorption of electromagnetic radiation;

(c) by absorption of electromagnetic radiation of particular frequency;

(b) by absorption of any electromagnetic radiation;

(a) by emission of electromagnetic radiation;

Q 3. What does negative sign in the electronic energy for hydrogen atom convey;

(a) Energy of electron when \(\mathrm{n}=\infty\);

(b) The energy of electron in the atom is lower than the energy of a free electron in motion;

(c) The energy of electron in the atom is lower than the energy of a free electron of rest;

(d) The energy of electron decreases as it moves away from nucleus;

Q 4. An ion has 18 electrons in the outermost shell, it is;

(a) \(\mathrm{Cu}^{+}\);

(b) \(\mathrm{Th}^{4+}\);

(c) \(\mathrm{Cs}^{+}\);

(d) \(\mathrm{K}^{+}\);

Q 5. In a given atom no two electrons can have the same values for all the four quantum numbers This is called;

(a) Hund's Rule;

(b) Aufbau principle;

(c) Uncertainty principle;

(d) Pauli's exclusion principle;

Q 6. For which element, the valence electron will be present in the highest energy orbital;

(a) \({ }_{3} \mathrm{Li}\);

(b) \({ }_{16} \mathrm{~S}\);

(c) \({ }_{20} \mathrm{Ca}\);

(d) \({ }_{21} \mathrm{Sc}\);

Q 7. The electron was shown experimentally to have wave properties by [1994];

(d) Schrodinger.;

(c) N. Bohr;

(b) Davisson and Germer;

(a) de Broglie;

Q 8. The ions \(\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Na}^{+}, \mathrm{Mg}^{2+}\) and \(\mathrm{Al}^{3+}\) are isoelectronic Their ionic radii show [2003];

(a) A decrease from \(\mathrm{O}^{2-}\) to \(\mathrm{F}^{-}\)and then increase from \(\mathrm{Na}^{+}\)to \(\mathrm{Al}^{3+}\);

(b) A significant increase from \(\mathrm{O}^{2-}\) to \(\mathrm{Al}^{3+}\);

(c) A significant decrease from \(\mathrm{O}^{2-}\) to \(\mathrm{Al}^{3+}\);

(d) An increase from \(\mathrm{O}^{2-}\) to \(\mathrm{F}^{-}\)and then decrease from \(\mathrm{Na}^{+}\)to \(\mathrm{Al}^{3+}\);

Q 9. Two electrons occupying the same orbital are distinguished by \([2016]\);

(a) Principal quantum number;

(b) Magnetic quantum number;

(c) Azimuthal quantum number;

(d) Spin quantum number;

Q 10. The ion that is isoelectronic with \(\mathrm{CO}\) is [1997];

(a) \(\mathrm{CN}^{-}\);

(b) \(\mathrm{O}_{2}{ }^{+}\);

(c) \(\mathrm{O}_{2}^{-}\);

(d) \(\mathrm{N}_{2}{ }^{+}\);

Bohr's atomic model


Niels Bohr’s model introduced the idea of quantized electron orbits in 1913. Electrons occupy specific energy levels, and they emit or absorb energy when transitioning between levels. Bohr’s model explained the spectral lines of hydrogen but had limitations when applied to multi-electron atoms.

 

Numerical Example:

- Calculate the energy difference when an electron in a hydrogen atom transitions from \( n = 3 \) to \( n = 2 \). 

  Solution: 

  \( \Delta E = 13.6 \left( \frac{1}{2^2} - \frac{1}{3^2} \right) = 1.89 \, \text{eV} \).

Questions

Q 1. An element has atomic number 11 and mass number 24 What does the nucleus contain?;

(a) 11 protons, 13 neutrons;

(b) 11 protons, 13 neutrons, 13 electrons;

(c) 13 protons, 11 neutrons;

(d) 13 protons, 11 electrons;

Q 2. A' represents mass no and \(Z\( represents atomic no then \(\alpha\( - decay is characterized by;

(a) Z increases by 2 , A decreases by 4;

(b) Z decreases by 2 , A increases by 4;

(c) Z decreases by 2 , A decreases by 4;

(d) Z increases by 2 , \(\mathrm{A}\( increases by 4 .;

Q 3. Atoms with same mass number but different atomic numbers are called;

(a) isotopes;

(b) isobars;

(c) isochores;

(d) None of these;

Q 4. What is the difference between two species if one has atomic mass =14 and atomic number =7 whereas the other has atomic mass =14 and atomic number =6 ?;

(a) Neutrons;

(b) Protons;

(c) Electrons;

(d) All of these;

Q 5. From the data given below \(A, B, C \text{ and } D \text{ respectively are,} \\ A: \, 10 e^{-}, \text{ atomic no. 11} \\ B: \, 10 e^{-}, \text{ atomic no. 6} \\ C: \, 10 e^{-}, \text{ atomic no. 10} \\ D: \, 10 e^{-} \);

(a) \(\mathrm{Na}^{+}, \mathrm{C}^{4-}, \mathrm{Ne}, \mathrm{F}^{-}\);

(b) \(\mathrm{C}^{4-}, \mathrm{Ne}, \mathrm{Na}^{-}, \mathrm{F}^{-}\);

(c) \(\mathrm{F}^{-}, \mathrm{Na}^{+}, \mathrm{Ne}, \mathrm{C}^{4-}\);

(d) \(\mathrm{F}^{-}, \mathrm{Na}^{+}, \mathrm{C}^{4-}, \mathrm{Ne}\);

Q 6. In hydrogen atomic spectrum, a series limit is found at \(12186 3 \mathrm{~cm}^{-1}\) Then it belong to;

(a) Lyman series;

(b) Balmer series;

(c) Paschen series;

(d) Brackett series;

Electromagnetic radiation


Electromagnetic radiation consists of waves with electric and magnetic fields oscillating perpendicular to each other. The energy of electromagnetic radiation is given by \( E = h\nu \), where \( \nu \) is the frequency. This radiation spans a broad spectrum, from radio waves to gamma rays, and is involved in phenomena like the photoelectric effect and atomic spectra.

 

Numerical Example:

- Calculate the energy of a photon with a frequency of \( 5 \times 10^{14} \) Hz. 

  Solution: 

  \( E = 6.626 \times 10^{-34} \times 5 \times 10^{14} = 3.313 \times 10^{-19} \) J.

 

Questions

Q 1. When a metal surface is exposed to solar radiations;

(a) The emitted electrons have energy less than a maximum value of energy depending upon frequency of incident radiations;

(b) The emitted electrons have energy less than maximum value of energy depending upon intensity of incident radiation;

(c) The emitted electrons have zero energy;

(d) The emitted electrons have energy equal to energy of photons of incident light;

Q 2. What will be the difference between electromagnetic radiation shown in \(\mathrm{A}\) and \(\mathrm{B}\) respectively? (A) (B) (i) Velocity (ii) Wavelength (iii) Frequency (iv) Energy;

(a) (ii) only;

(b) (ii) and (iv);

(c) (ii), (iii) and (iv);

(d) (iv) only;

Heisenberg's uncertainty principle


The uncertainty principle, formulated by Werner Heisenberg in 1927, states that it is impossible to know both the exact position and momentum of a particle simultaneously. The principle is expressed as \( \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \). It explains the limitations of measuring quantum systems and is foundational in quantum mechanics.

 

Numerical Example:

- Calculate the uncertainty in momentum if the uncertainty in position is \( 1 \times 10^{-10} \) m. 

  Solution: 

  \( \Delta p \geq \frac{6.626 \times 10^{-34}}{4\pi \times 1 \times 10^{-10}} = 5.27 \times 10^{-25} \) kg·m/s.

Questions

Q 1. Heisenberg uncertainty principle can be explained as;

(a) \(\Delta x \geq \frac{\Delta P \times h}{4 \pi}\);

(b) \(\Delta x \times \Delta P \geq \frac{h}{4 \pi}\);

(c) \(\Delta x \times \Delta P \geq \frac{h}{\pi}\);

(d) \(\Delta P \geq \frac{\pi h}{\Delta x}\);

Q 2. Heisenberg's uncertainity principle is applicable to;

(a) atoms only;

(b) electron only;

(c) nucleus only;

(d) any moving object;

Quantum mechanical model of atom


Developed by Schrödinger, this model describes electrons as wavefunctions rather than fixed particles. Electrons occupy orbitals, which are probability distributions. The model uses quantum numbers to describe the electron’s position and energy. The four quantum numbers—principal \( n \), angular momentum \( l \), magnetic \( m_l \), and spin \( m_s \)—define each electron’s state and behavior

within an atom. The quantum mechanical model successfully explains the electronic structure of multi-electron atoms and the shapes of orbitals.

 

Numerical Example:

- Assign the quantum numbers for an electron in the 3d orbital. 

  Solution: 

  \( n = 3, l = 2, m_l = -2, -1, 0, +1, +2, m_s = +\frac{1}{2} \) or \( -\frac{1}{2} \).

 

Questions

Q 1. The following quantum numbers are possible for how many orbital(s) \(n=3, l=2, \mathrm{~m}=+2\) ?;

(a) 1;

(b) 3;

(c) 2;

(d) 4;

Q 2. The following quantum numbers are possible for how many orbital (s) \(n=3, l=2, m=+2\) ? [2001];

(a) 1;

(b) 3;

(c) 2;

(d) 4;

Atomic spectra and line spectra


When electrons in an atom transition between energy levels, they emit or absorb light at specific wavelengths, producing atomic spectra. These spectra consist of discrete lines, corresponding to particular transitions. In the hydrogen atom, spectral lines are grouped into series (Lyman, Balmer, Paschen, etc.). The energy difference between levels is given by the formula:

 

\[

\Delta E = h\nu = 13.6 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \, \text{eV}

\]

 

where \( n_1 \) and \( n_2 \) are the initial and final principal quantum numbers.

 

Numerical Example:

- Calculate the wavelength of light emitted when an electron in a hydrogen atom transitions from \( n = 4 \) to \( n = 2 \) (Balmer series). 

  Solution: 

  \( \Delta E = 13.6 \left( \frac{1}{2^2} - \frac{1}{4^2} \right) = 2.55 \, \text{eV} \). 

  Using \( E = \frac{hc}{\lambda} \), 

  \( \lambda = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{2.55 \times 1.6 \times 10^{-19}} = 486 \, \text{nm} \).

Questions

Q 1. The \(\mathrm{Li}^{2+}\) ion is moving in the third stationary state, and its linear momentum is \(7 3 \times 10^{-34} \mathrm{~kg} \mathrm{~ms}^{-1}\) Calculate its angular momentum;

(a) \(1.158 \times 10^{-45} \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\);

(b) \(11.58 \times 10^{-48} \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\);

(c) \(11.58 \times 10^{-47} \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\);

(d) \(12 \times 10^{-45} \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-1}\);

Q 2. If uncertainty in position and momentum are equal, then uncertainty in velocity is :;

(a) \(\frac{1}{2 m} \sqrt{\frac{h}{\pi}}\);

(b) \(\sqrt{\frac{h}{2 \pi}}\);

(c) \(\frac{1}{m} \sqrt{\frac{h}{\pi}}\);

(d) \(\sqrt{\frac{h}{\pi}}\);

Q 3. The five \(d\)-orbitals are designated as \(d_{x y}, d_{y z}, d_{x z}, d_{x^{2}-y^{2}}\) and \(d_{z^{2}}\) Choose the correct statement;

(a) The shapes of the first three orbitals are similar but that of the fourth and fifth orbitals are different;

(b) The shapes of all five \(d\)-orbitals are similar;

(c) The shapes of the first four orbitals are similar but that of the fifth orbital is different;

(d) Ths shapes of all five \(d\)-orbitals are different;

Q 4. If uncertainty in position and momentum are equal, then uncertainty in velocity is : [2008];

(a) \(\frac{1}{2 m} \sqrt{\frac{h}{\pi}}\);

(b) \(\sqrt{\frac{h}{2 \pi}}\);

(c) \(\frac{1}{m} \sqrt{\frac{h}{\pi}}\);

(d) \(\sqrt{\frac{h}{\pi}}\);

Q 5. Orbital having 3 angular nodes and 3 total nodes is [NEET Odisha 2019];

(a) \(6 d\);

(b) \(5 p\);

(c) \(3 d\);

(d) \(4 f\);

Q 6. The graph between \(|\psi|^{2}\) and \(r\) (radial distance) is shown below This represents;

(a) \(3 s\)-orbital;

(b) \(2 s\)-orbital;

(c) \(1 s\)-orbital;

(d) \(2 p\)-orbital;

Topics

Discovery of neutron

Proton characteristics

Pauli exclusion principle

Structure of subatomic particles

Rutherford's nuclear model

de Broglie relation

Thomson's model of atom

Discovery of electron

Bohr's atomic model

Electromagnetic radiation

Heisenberg's uncertainty principle

Quantum mechanical model of atom

Atomic spectra and line spectra

Media