1.
Calculate the number of protons, neutrons, and electrons in $^{35}_{17}\mathrm{Cl}$ and $^{80}_{35}\mathrm{Br}$.
2.
An atom of an element contains 29 electrons and 35 neutrons. Deduce (i) the number of protons and (ii) the mass number of the element.
3.
In Rutherford's scattering experiment, which subatomic particle was used to bombard the thin gold foil, and what conclusion was drawn from the observation that a very small fraction of particles bounced back?
4.
Calculate the mass and charge of one mole of electrons.
5.
Arrange the fundamental particles (electron, proton, neutron, alpha particle) in increasing order of their specific charge (e/m ratio).
6.
Calculate the wavelength, frequency, and wavenumber of a light wave whose period is $2.0 \times 10^{-10}$ s.
7.
Find the energy of a photon which corresponds to light of frequency $3 \times 10^{15}$ Hz. (Given $h = 6.626 \times 10^{-34}$ J s)
8.
Calculate the energy of one mole of photons of radiation whose frequency is $5 \times 10^{14}$ Hz.
9.
A 100 watt bulb emits monochromatic light of wavelength 400 nm. Calculate the number of photons emitted per second by the bulb.
10.
The Vividh Bharati station of All India Radio, Delhi, broadcasts on a frequency of 1,368 kHz. Calculate the wavelength of the electromagnetic radiation emitted by the transmitter.
11.
The threshold frequency ($\nu_0$) for a metal is $7.0 \times 10^{14}$ s$^{-1}$. Calculate the kinetic energy of an electron emitted when radiation of frequency $\nu = 1.0 \times 10^{15}$ s$^{-1}$ hits the metal.
12.
A photon of wavelength $4 \times 10^{-7}$ m strikes on metal surface, the work function of the metal being 2.13 eV. Calculate (i) the energy of the photon (eV), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron.
13.
When light with a wavelength of 400 nm falls on the surface of potassium metal, electrons with a kinetic energy of $0.85$ eV are emitted. Find the work function of potassium in Joules.
14.
Why does the number of ejected photoelectrons increase with the intensity of incident light, whereas their kinetic energy remains independent of intensity?
15.
What is the radius of the first orbit of $\mathrm{He^+}$ ion? Compare it with the radius of the first orbit of Hydrogen atom.
16.
Calculate the energy associated with the first orbit of $\mathrm{He^+}$. What is the radius of this orbit?
17.
Calculate the wavelength of the spectral line obtained in the spectrum of $\mathrm{Li^{2+}}$ ion when the transition takes place between two levels whose principal quantum numbers are $n_2 = 3$ and $n_1 = 1$.
18.
What is the maximum number of emission lines when the excited electron of an H atom in $n = 6$ drops to the ground state?
19.
Calculate the wavenumber for the shortest wavelength transition in the Balmer series of atomic hydrogen. (Given $R_H = 109677$ cm$^{-1}$)
20.
Find the ratio of the velocity of an electron in the first Bohr orbit of Hydrogen to its velocity in the second Bohr orbit of $\mathrm{Li^{2+}}$.
21.
The ionization energy of $\mathrm{He^+}$ is $19.6 \times 10^{-18}$ J atom$^{-1}$. Calculate the energy of the first stationary state of $\mathrm{Li^{2+}}$.
22.
If the velocity of an electron in a Bohr orbit is $V$, what will be its velocity in the next higher orbit of the same atom?
23.
Calculate the de Broglie wavelength of an electron traveling with a velocity equal to 1% of the speed of light.
24.
A macroscopic ball of mass 0.1 kg is moving with a velocity of 10 m/s. Calculate its de Broglie wavelength and explain why the wave nature of this ball is not observable.
25.
Two particles A and B are in motion. If the momentum of A is half of that of B, and if the wavelength of A is $5 \times 10^{-8}$ m, calculate the wavelength of B.
26.
Calculate the kinetic energy of a moving electron which has a wavelength of 4.8 pm.
27.
Derive the relationship between the de Broglie wavelength ($\lambda$) and the Kinetic Energy (K.E.) of a particle.
28.
A golf ball has a mass of 40g, and a speed of 45 m/s. If the speed can be measured within accuracy of 2%, calculate the uncertainty in the position.
29.
If the position of an electron is measured with an accuracy of $\pm 0.002$ nm, calculate the uncertainty in the momentum of the electron.
30.
Show that if the uncertainty in the position of a moving particle is equal to its de Broglie wavelength, its velocity is completely uncertain (i.e., $\Delta v \approx v/4\pi$).
31.
Why is Heisenberg's uncertainty principle significant only for microscopic particles and negligible for macroscopic objects? Provide mathematical reasoning.
32.
List all the possible values of $l$ and $m_l$ for $n = 3$. How many total orbitals are present in the 3rd shell?
33.
Designate the orbitals having: (a) $n=2, l=1$ (b) $n=4, l=0$ (c) $n=5, l=3$ (d) $n=3, l=2$.
34.
Calculate the total number of angular nodes and radial nodes present in a 4d orbital.
35.
What is the maximum number of electrons in an atom that can have the quantum numbers $n=4, m_s=-1/2$?
36.
Write the formula for orbital angular momentum. Calculate its value for a 3p electron.
37.
Identify which of the following sets of quantum numbers are not possible and state the reason: (a) $n=1, l=0, m_l=0, m_s=-1/2$ (b) $n=3, l=3, m_l=-3, m_s=+1/2$ (c) $n=2, l=1, m_l=0, m_s=+1$.
38.
State Pauli's Exclusion Principle. Explain how it determines the maximum capacity of an orbital to hold electrons.
39.
Write the complete electronic configuration of $\mathrm{Cr}$ (Z=24) and $\mathrm{Cu}$ (Z=29). Explain the reason for their exceptional configurations.
40.
Determine the number of unpaired electrons in the following ions: (a) $\mathrm{Fe^{3+}}$ (Z=26) (b) $\mathrm{Mn^{2+}}$ (Z=25) (c) $\mathrm{Ni^{2+}}$ (Z=28).
41.
Based on Hund's Rule of Maximum Multiplicity, write the orbital diagram configuration for Nitrogen (Z=7) and Oxygen (Z=8).
42.
Calculate the spin-only magnetic moment of a divalent ion in aqueous solution if its atomic number is 25. (Formula: $\mu = \sqrt{n(n+2)}$ BM)
43.
Arrange the following orbitals in increasing order of their energy: 4d, 5p, 5s, 6s. (Use $(n+l)$ rule).
