by Rajan M V | Oct 17, 2015 | Miscellaneous

Problem 6.84: A thin symmetric convex lens of refractive index $1.5$ and radius of curvature $0.3 \:m$ is put in water of refractive index $\frac{4}{3}$. What will be its focal length? Solution: Focal length of a lens made out of a material of refractive index $n_1$...
by Rajan M V | Oct 16, 2015 | Miscellaneous

Problem 6.83:At what angle should a ray of light be incident on the face of a prism of refracting angle $60^o$ so that it just suffers total internal reflection at the other face? The refractive index of the material of the prism is $\sqrt{2}$. Solution: Total...
by Rajan M V | Oct 15, 2015 | Miscellaneous

Problem 6.82:A point object is placed at a distance of $15\:cm$ from a convex lens of focal length $10\:cm$. On the other side of the lens a concave mirror of radius of curvature $20\:cm$ is placed at a distance of $50\:cm$ facing the convex lens. Find the position...
by Rajan M V | Oct 14, 2015 | Miscellaneous

Problem 6.81:A ray falls at an angle of $30^0$ with the plane of a flat mirror. Find the angle through which it deviates? Solution: The ray will get reflected by the flat mirror. In doing so it obeys law of reflection where the angle of reflection is equal to the...
by Rajan M V | Oct 6, 2015 | Optics

Problem 6.80:Determine the focal length of a concave mirror of radius of curvature $40\:cm$ in air and in water. Refractive index of water is approximately $\frac{4}{3}$. Solution: Focal length a mirror of radius of curvature $R$ in air is...
by Rajan M V | Sep 27, 2015 | Modern physics

Problem 7.100:Using Bohr theory in hydrogen atom it was found that the total energy of an electron is $-1.51\:eV$. Determine its angular momentum. Solution: According to Bohr theory total energy of orbiting electron is given by the equation...
by Rajan M V | Sep 21, 2015 | Modern physics

Problem 7.99: The orbital angular momentum of an electron in a Hydrogen-like atom is $\frac{3h}{2\pi}$. Calculate its principal quantum number. Solution: According to Bohr’s second postulate, angular momentum of electron in the hydrogen atom with respect to the...
by Rajan M V | Sep 16, 2015 | Modern physics

Problem 7.98: A hypothetical nucleus $_{92}A^{238}$ emits an alpha particle and a then a beta particle. Find the atomic number and mass number of the new nucleus formed. Solution: When a nucleus emits alpha particle mass number decreases by four and atomic number by...
by Rajan M V | Sep 10, 2015 | Modern physics

Problem 7.97: Explain how non fissile uranium-238 is converted into fissile plutonium-239. Solution: Initially $U^{238}$ is bombarded with a slow neutron. $U^{238}$ will change to $U^{239}$. $_{92}U^{238}\:+\:_0n^1\:=\:_{92}U^{239}$. Nucleus of $U^{239}$ is highly...
by Rajan M V | Sep 8, 2015 | Miscellaneous

Problem 7.96: The half-life of $_90 ^38Sr$ is $28$ years. What is the disintegration rate of $15 \:mg$ of this isotope? Solution: If there are $N$ number of nucleus of a radioactive material, then the rate of disintegration at that instant is given by...
by Rajan M V | Sep 3, 2015 | Modern physics

Problem 7.95: A radioactive isotope has a half-life of $ T$ years. How long will it take the isotope to reduce to $3.125\:%$ of its original value? Solution: Let there be $N_o$ number of nuclei in a radioactive sample with half life $T$. Let $N$ be the number of...
by Rajan M V | Sep 2, 2015 | Modern physics

Problem 7.94: Audio sine waves of $3\: kHz$ frequency are used to amplitude modulate a carrier signal of $1.5 \:MHz$. Determine the side band frequencies. Solution: In amplitude modulation, if $f_c$ is the frequency of the carrier and $f_m$ is the frequency of the...
by Rajan M V | Aug 17, 2015 | Modern physics

Problem 7.93:X-rays produced by electrons of $50 \:keV$ kinetic energy striking a lead target. What would be the wavelength of the most energetic rays ? Solution: Energy of a photon is given by the equation $E\:=\:\frac{hc}{\lambda}$. Most energetic rays are produced...
by Rajan M V | Aug 13, 2015 | Modern physics

Problem 7.92:The deuterium–tritium fusion can be expressed by the equation $_1^2H\:+\:_1^3H\rightarrow_2^4He\:+\:n$. Calculate the energy released in MeV in this reaction. Given are the nuclear masses:$m(_1^2H)\:=\:2.014102 \:u$, $m(_1^3H)\:=\:3.016049\: u$,...
by Rajan M V | Aug 12, 2015 | Modern physics

Problem 7.91: Obtain the binding energy of the nuclei $ _{26}Fe^{56}$. Given that mass of $ _{26}Fe^{56}\:=\: 55.934939\: u$, mass of proton $1.00727\:u$ and mass of neutron $1.00866\:u$. Solution: To form a nucleus of a certain charge and mass,by joining...
by Rajan M V | Aug 10, 2015 | Modern physics

Problem 7.90:The separation between two deuterons must be about $1.0\times 10^{-14}\: m$ for the attractive nuclear force to overcome the repulsive Coulomb force. Calculate the height of the potential barrier due to the repulsive force. Solution: Potential barrier...
by Rajan M V | Aug 9, 2015 | Modern physics

Problem 7.89: When cesium metal is illuminated with light of wavelength $300 \:nm$, the photo electrons emitted have a maximum kinetic energy of $2.23 \:eV$. Find the work function of cesium. Solution: We can use Einstein’s photoelectric equation to solve this...
by Rajan M V | Aug 8, 2015 | Modern physics

Problem 7.88:What is the wavelength of a photon of energy $2.40\: eV$? Solution: Energy of a photon in light of frequency $\nu$ is given by $E\:=\:h\nu$ where $h$ is Planck’s constant which is equal to $6.62\times 10^{-34}\:Js$. In terms of wavelength, $\lambda$ this...