If the velocity of the electron in Bohr’s first orbit is $2.19 \times 10^6$ ms$^{-1}$, calculate the de Broglie wavelength associated with it.

Find energy of each of the photons which (i) correspond to light of frequency $3 \times 10^{15}$ Hz.

Indicate the number of unpaired electrons in : (d) Fe and

(ii) Find (a) the total number and (b) the total mass of neutrons in 7 mg of $^{14}$C. (Assume that mass of a neutron = $1.675 \times 10^{-27}$ kg).

Using s, p, d notations, describe the orbital with the following quantum numbers. (b) $n = 3; l=1$

Neon gas is generally used in the sign boards. If it emits strongly at 616 nm, calculate (a) the frequency of emission, (b) distance traveled by this radiation in 30 s (c) energy of quantum and (d) number of quanta present if it produces 2 J of energy.

Electromagnetic radiation of wavelength 242 nm is just sufficient to ionise the sodium atom. Calculate the ionisation energy of sodium in kJ mol$^{-1}$.

The mass of an electron is $9.1 \times 10^{-31}$ kg. If its K.E. is $3.0 \times 10^{-25}$ J, calculate its wavelength.

Explain, giving reasons, which of the following sets of quantum numbers are not possible. (e) $n$ = 3, $l$ = 3, $m_l$ = –3, $m_s$ = + $\frac{1}{2}$

Write the complete symbol for the atom with the given atomic number ($Z$) and atomic mass ($A$) (ii) $Z$ = 92, $A$ = 233.

In Rutherford’s experiment, generally the thin foil of heavy atoms, like gold, platinum etc. have been used to be bombarded by the $\alpha$-particles. If the thin foil of light atoms like aluminium etc. is used, what difference would be observed from the above results ?

The bromine atom possesses 35 electrons. It contains 6 electrons in 2p orbital, 6 electrons in 3p orbital and 5 electron in 4p orbital. Which of these electron experiences the lowest effective nuclear charge ?

Calculate the wavelength, frequency and wavenumber of a light wave whose period is $2.0 \times 10^{-10}$ s.

(ii) List the quantum numbers ($m_l$ and $l$) of electrons for 3d orbital.

Following results are observed when sodium metal is irradiated with different wavelengths. Calculate (a) threshold wavelength and, (b) Planck’s constant. $\lambda$ (nm) 500 450 400, $v \times 10^{-5}$ (cm s$^{-1}$) 2.55 4.35 5.35

Write the complete symbol for the atom with the given atomic number ($Z$) and atomic mass ($A$) (i) $Z$ = 17, $A$ = 35.

(a) How many subshells are associated with $n$ = 4 ?

What is the maximum number of emission lines when the excited electron of a H atom in $n$ = 6 drops to the ground state?

The quantum numbers of six electrons are given below. Arrange them in order of increasing energies. If any of these combination(s) has/have the same energy lists: 1. $n$ = 4, $l$ = 2, $m_l$ = –2 , $m_s$ = –1/2 2. $n$ = 3, $l$ = 2, $m_l$ = 1 , $m_s$ = +1/2 3. $n$ = 4, $l$ = 1, $m_l$ = 0 , $m_s$ = +1/2 4. $n$ = 3, $l$ = 2, $m_l$ = –2 , $m_s$ = –1/2 5. $n$ = 3, $l$ = 1, $m_l$ = –1 , $m_s$ = +1/2 6. $n$ = 4, $l$ = 1, $m_l$ = 0 , $m_s$ = +1/2

$2 \times 10^8$ atoms of carbon are arranged side by side. Calculate the radius of carbon atom if the length of this arrangement is 2.4 cm.