Chapter 3

$$ \begin{aligned} &\text { Calculate the wavelength of } 1000 \mathrm{~kg} \text { rocket moving with a velocity }\\\ &\text { of } 3000 \mathrm{~km} \text { per hour. }\left(h=6.626 \times 10^{-34} \mathrm{Js}\right) \text { . } \end{aligned} $$

A \(1.0 \mathrm{~g}\) particle is shot from a gun with velocity of \(100 \mathrm{~m} / \mathrm{sec}\). Calculate its de Broglie wavelength.

$$ \begin{aligned} &\text { Calculate the wavelength of an electron moving with a velocity of }\\\ &2.05 \times 10^{7} \mathrm{~ms}^{-1} \end{aligned} $$

A photon of wavelength \(4 \times 10^{-7} \mathrm{~m}\) strikes on metal surface, the work function of the metal being \(2.13 \mathrm{eV}\). Calculate : (i) the energy of the photon (eV), (ii) the kinetic energy of the emission, and (iii) the velocity of the photoelectron \(\left(1 \mathrm{eV}=1.6020 \times 10^{-19} \mathrm{~J}\right)\).

The minimum energy required for the emission of photoelectron from the surface of a metal is \(4.95 \times 10^{-19} \mathrm{~J}\). Calculate the critical frequency and the corresponding wavelength of the photon required to eject the electron. \(h=6.6 \times 10^{-34} \mathrm{~J} \mathrm{sec}\).

Light of wavelength \(300 \times 10^{-9} \mathrm{~m}\) strikes a metal surface with photoelectric work function of \(2.13 \mathrm{eV}\). Find out the kinetic energy of the most energetic photoelectron.

A metal surface of threshold frequency \(5.3 \times 10^{14} \mathrm{sec}^{-1}\) is exposed to a photon of radiation having energy \(3.5 \times 10^{-19} \mathrm{~J}\). Will it exhibit photoelectric effect?

Point out the followings: (a) How many energy subshells are possible in \(n=3\) level. (b) How many orbitals of all kinds are possible in \(n=3\) level.

How many electrons may enter the orbital denoted by (a) \(2 p\), (b) \(I\) s, (c) \(3 p\), (d) \(3 d\)

What values are assigned to quantum numbers \(n, l, m\) for : (a) \(3 \mathrm{~s}\), (b) \(4 p_{z}\) (c) \(4 d_{x^{2}-y^{2}}\) (d) \(5 d_{z^{2}}\)