Physics based Calculation Problems for Class 8

A student need to practice maths problems. Its helps in developing problem solving skills. The problems shall not be (i) too simple, (ii) too difficult or (iii) too many. Simple problems are boring, difficult problems discourages (at times), and too many problems don't leave time for fun.

I selected following problems on physics based calculations for my son studying in class 8.

1. The charge on an electron is $q=1.6\times10^{-19}$ Coulomb. The mass of the electron is $m=9.1\times10^{-31}$ kg. Find charge to mass ratio ($q/m$) for an electron.
2. The electrostatic force between two particles of charges $q_1$ and $q_2$ separated by a distance $r$ is given by \begin{align} F_e=\frac{1}{4\pi\epsilon_0} \frac{q_1 q_2}{r^2}. \end{align} Take $\epsilon_0=9\times10^{-12}$, $q_1=1.6\times10^{-19}$, $q_2=1.6\times10^{-19}$ and $r=10^{-15}$ to find electrostatic repulsion force between two protons in a nucleus. The force you get is in Newton.
3. The gravitational force between two particles of masses $m_1$ and $m_2$ separated by a distance $r$ is given by \begin{align} F_g= \frac{G m_1 m_2}{r^2}. \end{align} Take $G=6.67\times10^{-11}$, $m_1=1.67\times10^{-27}$, $m_2=1.67\times10^{-27}$ and $r=10^{-15}$ to find gravitational attraction force between two protons in a nucleus. The force you get is in Newton.
4. Find $F_e/F_g$ for two protons. The electrostatic force is much much larger than the gravitational force.
5. The average kinetic energy of an atom at temperature $T$ Kelvin is given by $E=\frac{3}{2}kT$, where $k=1.38\times10^{-23}$. Calculate the average kinetic energy of an atom at room temperature (T = 300 Kelvin). The energy you get is in Joule. The kinetic energy due to temperature is also called thermal energy.
6. The energy is converted from Joule to electron-volt (a useful unit in modern physics) by dividing energy in Joule by charge of an electron. Convert the average kinetic energy of an atom at room remperature into electron-volt.
7. The temperature at the core of the sun is $1.5\times10^{7}$ Kelvin. Find average kinetic energy of a proton at this temperature. The electrostatic potential energy between two charges $q_1$ and $q_2$ separated by a distance $r$ is given by \begin{align} U=\frac{q_1 q_2}{4\pi\epsilon_0 r}. \end{align} Find the distance between two protons at which their electrostatic potential energy is equal to their average kinetic energy at the core of the sun.
8. The energy of a photon of wavelength $\lambda$ is given by \begin{align} E=\frac{hc}{\lambda}, \end{align} where $h=6.64\times10^{-34}$ and $c=3\times10^{8}$. The energy you get is in Joule. Find energy of a photon of visible light of wavelength $\lambda=5\times10^{-7}$ metre. Convert this energy into electron-volt.
9. Find the energy of a Ultra Vilot (UV) light photon of wavelength $\lambda=10^{-7}$ metre. Convert this energy in electron-volt. UV photons of this energy can eject electrons from the surface of metals. This phenomenon is called photo-electric effect.
10. The solar energy falling on one square metre area of the earth in one second is 1400 Joule. Assume that all photons are of wavelenegth $5\times10^{-7}$. How many photons are falling in this area in one second.
11. Avogadro number is the number of carbon atoms in 12 gram of carbon. The carbon atom has 6 protons, 6 neutrons, and 6 electrons. The mass of the electron is negligible in comparison to that of proton. The mass of the neutron is approximately equal to the mass of the proton. Can you find the approximate value of Avogadro number. It is very large.