Which ion has the stable electronic configuration? Ni²⁺ or Fe³⁺.

How many electrons in an atom may have the following quantum numbers? 
(a) n = 4; m_s = -1/2 (b) n = 3, l = 0.

Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

An ion with mass number 56 contains 3 units of positive charge and 30.4% more neutrons than electrons. Assign symbol to the ion.

The uncertainty in the position of a moving bullet of mass 10 g is 10^-5 m. Calculate the uncertainty in its velocity?

What are the conclusions of Rutherford's α-rays scattering experiment?

What are the limitations of Bohr's atom model?

Illustrate the significance of de Broglie equation with an iron ball and an electron.
(i) 6.626 kg iron ball moving with 10 ms^-1.
(ii) An electron moving at 72.73 ms^-1.

Explain Davisson and Germer experiment.

Calculate the uncertainty in velocity of an electron in hydrogen atom assuming the position of the electron in first orbit (0.529\(\mathring A\)) is determined with the accuracy of 0.5% of the radius.

Write a note about principal quantum number.

Explain about azimuthal quantum number.

Draw the shapes of 1s, 2s and 3s orbitals.

Calculate the wavelength of an electron moving with a velocity of 2.05 x 10⁷ ms^-1.

The mass of an electron is 9.1\(\times\)10^-31 kg.If its kinetic energy is 3.0 \(\times\) 10^-25J, calculate its wavelength.

The uncertainty in the position and velocity of a particle are 10^-10 m and 5.27 x 10^-24ms^-1respectively. Calculate the mass of the particle.

With what velocity must an electron travel so that its momentum is equal to that of a photon of wavelength = 5200\(\mathring{A}\) ?

Using Aufbau principle, write the ground state electronic configuration of following atoms.
(i) Boron (Z = 5)
(ii) Neon (Z = 10)
(iii) Aluminium (Z = 13)
(iv) Chlorine (Z = 17)
(v) Calcium (Z = 20)
(vi) Rubidium (Z = 37)

Calculate the de Broglie wavelength of an electron moving with 1% of the speed of light?

What is the wavelength for the electron accelerated by 1.0 x 10⁴ volts?

In a hydrogen atom, the energy of an electron in first Bohr's orbit is 13.12 x 10⁵ J mol^-1 . What is the energy required for its excitation to Bohr's second orbit?

From the following sets of quantum numbers, state which are possible. Explain why the others are not possible.
n = 0, l = 0, m_l = 0, \(m_s=+\frac{1}{2}\) 

From the following sets of quantum numbers, state which are possible. Explain why the others are not possible.
n = 1,l = 1,m_l = 0,\(m_s=+\frac{1}{2}\)

From the following sets of quantum numbers, state which are possible. Explain why the others are not possible.
\(n=1,l=1,m_l=0,m_s=+\frac{1}{2}\)

From the following sets of quantum numbers, state which are possible. Explain why the others are not possible.
\(n=1,l=0,m_l=+1,m_s=+\frac{1}{2}\)

From the following sets of quantum numbers, state which are possible. Explain why the others are not possible.
\(n=3,l=3,m_l=-3,m_s=+\frac{1}{2}\)

From the following sets of quantum numbers, state which are possible. Explain why the others are not possible.
\(n=3,l=1,m_l=0,m_s=+\frac{1}{2}\)

Dual behaviour of matter proposed by de Broglie led to the discovery of electron microscope often used for the highly magnified images of biological molecules and other type of material. If the velocity of the electron in this microscope is 1.6 x 10⁶ ms^-1, calculate de Broglie wavelength associated with this electron.

An element with mass number 81 contains 31. 7% more neutrons as compared to protons. Assign the symbol to the element.

The electron energy in hydrogen atom is given by E_n = (- 2.18 x 10^-18)/n² J. Calculate the energy required to remove an electron completely from the n = 2 orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Explain how effective nuclear charge us related with stability of the orbital.