Home
Class 12
PHYSICS
80^197Hg decay to 79^197Au through elect...

``_80^197Hg` decay to ``_79^197Au` through electron capture with a decay constant of 0.257 per day.(a)What other particle or particles are emitted in the decay?(b) assume that the electron is captured from the K shell. Use Moseley's law `sqrt v=a(Z-b)`with a `a=4.95xx10^7 s^(-1//2)` and b=1 to find the wavelenghth of the `K_a` x-ray emitted following the electron capature.

Text Solution

Verified by Experts

The correct Answer is:
A, B
(a) `p + e rarr n = v neutrino `
(b) `sqrt f = a (z-b) `
` sqrt (( c)/( lambda )) = 4.9.5 xx 10^(7) (79 - 1)`
` = 4.95 xx 10^(7) xx 78 `
` ( c ) /( lambda) = (4.95 xx 78)^(2) xx 10^(14) `
` lambda = (3 xx 10 ^(8) )/(149032 xx 10^(14)) `
` = 2 xx 10^(5) xx 10^(-5)`
` = 2 xx 1m = 20 pm `
Promotional Banner

Topper's Solved these Questions

  • THE NUCLEOUS

    HC VERMA|Exercise Objective 2|10 Videos

  • SPEED OF LIGHT

    HC VERMA|Exercise Exercises|3 Videos

  • THE SPECIAL THEORY OF RELATIVITY

    HC VERMA|Exercise Exercises|27 Videos

Similar Questions

Explore conceptually related problems

The positron is a fundamental particle with the same mass as that of the electron and with a charge equal to that of an electron but of opposite sign. When a positron and an electron collide, they may annihilate each other. The energy corresponding to their mass appears in two photons of equal energy. Find the wavelength of the radiation emitted. [Take : mass of electron = (0.5//c^(2))MeV and hc = 1.2 xx 10^(-12) MeV-m , where h is the Planck's constant and c is the velocity of light in air.

Two metallic plate A and B , each of area 5 xx 10^(-4)m^(2) , are placed parallel to each at a separation of 1 cm plate B carries a positive charge of 33.7 xx 10^(-12) C A monocharonatic beam of light , with photoes of energy 5 eV each , starts falling on plate A at t = 0 so that 10^(16) photons fall on it per square meter per second. Assume that one photoelectron is emitted for every 10^(6) incident photons fall on it per square meter per second. Also assume that all the emitted photoelectrons are collected by plate B and the work function of plate A remain constant at the value 2 eV Determine (a) the number of photoelectrons emitted up to i = 10s, (b) the magnitude of the electron field between the plate A and B at i = 10 s, and (c ) the kinetic energy of the most energotic photoelectrons emitted at i = 10 s whenit reaches plate B Negilect the time taken by the photoelectrons to reach plate B Take epsilon_(0) = 8.85 xx 10^(-12)C^(2)N- m^(2)

(a) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of 500 V with respect to the emitter. Ignore the small initial speeds of the electrons. The specific charge of the electron, i.e., its e/m is given to be 1.76 xx 10^(11) C kg^(-1) . (b) Use the same formula you employ in (a) to obtain electron speed for an collector potential of 10 MV. Do you see what is wrong ? In what way is the formula to be modified?

(a) Estimate the speed with which electrons emitted from a heated emitter of an evacuated tube impinge on the collector maintained at a potential difference of 500 V with respect to the emitter.Ignore the small initial speeds of the electrons.The specific charge of the electron ,i.e., its (e)/(m) is given to be 1.76xx10^(11)Ckg^(-1) (b) Use the same formula you employ in (a)to obtain electron speed for an collector potential of 10 MV.Do you see what is wrong ?in what way is the formula to be modified?

A single electron orbits a stationary nucleus of charge + Ze , where Z is a constant and e is the magnitude of electronic charge . It requires 47.2 eV to excite . Find a the value of Z b the energy required to excite the electron from the third to the fourth Bohr orbit. the wavelength of electromagnetic rediation required to remove the electron from the first Bohr orbit to infinity. d Find the KE,PE , and angular momentum of electron in the first Bohr orbit. e the redius of the first Bohr orbit [The ionization energy of hydrogen atom = 13.6 eV Bohr radius = 5.3 xx 10^(_11) m , "velocity of light" = 3 xx 10^(-8)jm s ^(-1) , Planck's constant = 6.6 xx 10^(-34)j - s]

Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm In the core of nucleus fusion reactor , the gas become plasma because of

Photoelectrons are emitted when 400 nm radiation is incident on a surface of work - function 1.9 eV. These photoelectrons pass through a region containing alpha -particles. A maximum energy electron combines with an alpha -particle to from a He^+ ion, emitting a single photon in this process. He^+ ions thus formed are in their fourth excited state. Find the energies in eV of the photons lying in the 2 to 4 eV range, that are likely to be emitted during and after the combination. [Take, h = 4.14xx10^(-15) eV -s]

Characteristic X-rays of frequency 4.2xx10^18 Hz are produced when transitions from L-shell to K-shell take place in a certain target material. Use Mosley's law to determine the atomic number of the target material. Given Rydberg constant R =1.1xx10^7 m^(-1) .

Consider a thin lens placed between a source (S) and an observer (O) (see figure) . Let the thicknes of the lens very as w(b) = w_0 - (b^2)/(alpha) , where b is the verticle distance from the pole. w_0 is constant. Using Fermat.s principle i.e. the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converage at a point O on the axis. Find the focal length. (ii) A gravitational lens may be assumed to have a varying width of the from w(b) = k_1 "ln" ((k_2)/(b)) b_("min") lt b lt b_("max") = k_1 "ln" ((k_2)/(b_"min")) b lt b_("min") Show that an observe will see an image of a point object as a right about the center of the lens with and angular radius beta=sqrt(((n-1)k_1(u)/(v))/(u+v))

Scientists are working hard to develop nuclear fusion reactor Nuclei of heavy hydrogen, _(1)^(2)H , known as deuteron and denoted by D , can be thought of as a candidate for fusion rector . The D-D reaction is _(1)^(2) H + _(1)^(2) H rarr _(2)^(1) He + n+ energy. In the core of fusion reactor, a gas of heavy hydrogen of _(1)^(2) H is fully ionized into deuteron nuclei and electrons. This collection of _1^2H nuclei and electrons is known as plasma . The nuclei move randomly in the reactor core and occasionally come close enough for nuclear fusion to take place. Usually , the temperature in the reactor core are too high and no material will can be used to confine the to plasma for a time t_(0) before the particles fly away from the core. If n is the density (number volume ) of deuterons , the product nt_(0) is called Lawson number. In one of the criteria , a reactor is termed successful if Lawson number is greater then 5 xx 10^(14) s//cm^(2) it may be helpfull to use the following boltzmann constant lambda = 8.6 xx 10^(-5)eV//k, (e^(2))/(4 pi s_(0)) = 1.44 xx 10^(-9) eVm Assume that two deuteron nuclei in the core of fusion reactor at temperature energy T are moving toward each other, each with kinectic energy 1.5 kT , when the seperation between them is large enough to neglect coulomb potential energy . Also neglate any interaction from other particle in the core . The minimum temperature T required for them to reach a separation of 4 xx 10^(-15) m is in the range

HC VERMA-THE NUCLEOUS-Exercises
  1. Natural water contains a small amount of tritium (1^3H). This isotope ...

    Text Solution

    |

  2. The count rate of nuclear radiation coming from a radioactive sample c...

    Text Solution

    |

  3. The half-life of K-40 is 1.30×10^ 9 year. A sample of 1.0 g of pure ...

    Text Solution

    |

  4. 80^197Hg decay to 79^197Au through electron capture with a decay const...

    Text Solution

    |

  5. A radioactive isotope is being produced at a constant rate dN//dt=R in...

    Text Solution

    |

  6. Consider the situation of the previous problem.suppose the production ...

    Text Solution

    |

  7. In an agriculture experiment, a solution containing 1 mole of a radioa...

    Text Solution

    |

  8. A vessel of vloume 125 cm^3 contains tritium (^3H,t(1//2)=12.3 y) at 5...

    Text Solution

    |

  9. 83^212Bi can disintegrate either by emitting an alpha -particle or by ...

    Text Solution

    |

  10. A sample contains a mixture of ^110Ag and ^108Ag isotopes each having ...

    Text Solution

    |

  11. A human body excretes (removes by waste discharge, sweating, etc,) cer...

    Text Solution

    |

  12. A charged capacitor of capacitance C is discharged through a resistanc...

    Text Solution

    |

  13. Radioactive isotopes are produced in a nuclear physics experiment at a...

    Text Solution

    |

  14. Calculate the energy released by 1 g of natural uranium assuming 200 M...

    Text Solution

    |

  15. A uranium rector develops thermal energy at a rate of 300 MW. Calculat...

    Text Solution

    |

  16. A town has a population of 1 million. The average electric power neede...

    Text Solution

    |

  17. Calculate the Q-values of the following fusion reactions: (a)1^2H+1^2H...

    Text Solution

    |

  18. Consider the fusion in helium plasma. Find the temperature at which th...

    Text Solution

    |

  19. Calculate the Q-values of the fusion reaction ^4(He)+^4He=^8(Be). I...

    Text Solution

    |

  20. Calculate the energy that can be obtained from 1 kg of water through t...

    Text Solution

    |