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## 6.84 Focal length of a converging lens

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 $n_1$...

## 6.83 Total internal reflection in a prism

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...

## 6.82 Combination of lens and mirror

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...

## 6.81 Deviation of ray in a plane mirror

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...

## 6.80 Focal length of a concave mirror

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...

## 7.100 Angular momentum of electron

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...

## 7.99 Principal quantum number

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...

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...

## 7.97 Conversion of uranium into plutonium

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...

## 7.96 Disintegration rate

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...

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...

## 7.94 SIde bands in Amplitude modulation

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...

## 7.93 Wavelength of X-rays

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...

## 7.92 Energy from fision reaction

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:$m(_1^2H)\:=\:2.014102 \:u$, $m(_1^3H)\:=\:3.016049\: u$,...

## 7.91 Binding energy of a nucleus

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...

## 7.90 Potential barrier between deuterons

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...

## 7.89 Work function of a metal

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...

## 7.88 Wavelength of photon

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...