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...

7.98 Radioactivity

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...

7.95 Radioactive disintegration

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...

7.87 Threshold frequency

Problem 7.87:Find the least frequency of incident light that will knock electrons out of the surface of a metal with a work function of $3 \:eV$. Solution: Work function $W$ is the minimum energy required to knock out an electron from  a metallic surface. In...

7.86 Momentum of elecron

Problem 7.86:What energy would an electron require in order to have the same momentum as an $8 \:MeV$ photon? Solution: Momentum of a photon of energy $(E)$ is given by $p\:=\:\frac{E}{c}$. Given that the energy of the photon $E\:=\:8 \:MeV$. This is equal to $8\times...

7.86 Maximum kinetic energy of photo elecrons

Problem 7.86:Find the maximum kinetic energy in $eV$ of electrons knocked out of a surface with a work function of $1.5\:eV$ by light of wavelength $6000\: Angstrom$. Solution: Photon in the light radiation will have an energy $E\:=\:\frac{hc}{\lambda}$. In this...

7.85 de Broglie wavelength

Problem 7.85: A particle of charge $q$ and mass $m$ is accelerated from rest through a small potential difference $V$. Find its de Broglie wavelength, assuming that the particle is non-relativistic. Solution: The charged particle was initially at rest. Its initial...

7.84 Kinetic energy of photo-electrons

Problem 7.84: Photo electrons released from zinc by ultraviolet light were stopped by a voltage of $4.3 \:V$. Find kinetic energy  of  these electrons.  Solution: When ultraviolet radiation with sufficient energy  is incident on zinc, photoelectrons are emitted. These...

7.83 Energy of photons

Problem 7.83:Radio waves have a frequency of the order of $1\:MHz$ to $100\: MHz$. What is the range of energies of these photons? Solution: Energy of photons in  a radio wave of frequency $\nu$ is equal to $h\nu$ joule. $h$ is Planck’s constant which is equal to...