Theory of Radioactive Disintegration

The half life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 hours would be

$\beta -$particle is emitted in a radio active reaction when

Two radioactive processes are given below

$\left(1\right) {}_{55}{}^{137}\mathrm{Cs}\stackrel{}{\to }{}_{56}{}^{137}\mathrm{Ba} \left(2\right) {}_{12}{}^{23}\mathrm{Mg}\stackrel{}{\to }{}_{11}{}^{23}\mathrm{Na}$

The $\mathrm{Q}-$values for these two processes are ${\mathrm{Q}}_1 \mathrm{and} {\mathrm{Q}}_2$ respectively, are given by

[Here $\mathrm{m}\left(\mathrm{X}\right)$ denotes the mass of an element of $\mathrm{X}$, ${\mathrm{m}}_{\mathrm{e}}$ denotes the mass of electron and ${\mathrm{Q}}_0$ denotes the amount energy liberated when 1 u of mass converts to energy]

Which of the $\mathrm{f}-$block group will change its group on emitting $\mathrm{\alpha } -$particle (alpha particle)
$(1{)}_{58}\mathrm{Ce} (2){}_{70}\mathrm{Lu} (3{)}_{90}\mathrm{Th} \left(4\right){}_{92}\mathrm{U}$
Correct answer is _____________.

A rock is found to contain $11.2\times {10}^{-5} \mathrm{mL}$ helium at STP and $2.38\times {10}^{-7} \mathrm{g}$ of uranium (${\mathrm{T}}_{50}$ of  ${}_{92}{}^{238}\mathrm{U}$ is $4.51\times {10}^9\mathrm{yr}$ and each${}_{92}{}^{238}\mathrm{U}$ is converted to ${}_{82}{}^{206} \mathrm{Pb}$).

${}_{92}{}^{238}\mathrm{U}⟶{}_{82}{}^{206} \mathrm{Pb}+8\mathrm{\alpha }+6\mathrm{\beta }$

Thus, age of rock is

THE THORIUM SERIES:

Find the number of correct statements about the given series.
1. It is one of the natural series found on earth.
2. The number of alpha particles obtained on disintegration of one${{}_{90}\mathrm{Th}}^{232}$ atom to get the stable product is $6$.
3. The number of beta particles obtained on disintegration of one ${}_{90}\mathrm{Th}^{228}$ atom to get the stable product is $2$ .
4. ${{}_{90}\mathrm{Th}}^{232}$ and ${}_{88}\mathrm{Ra}^{228}$ are isodiaphers.
5. The nuclear isomers of ${{}_{83}\mathrm{Bi}}^{212}$ gives ${}_{84}{\mathrm{P}}^{212}$ on beta decay and ${}_{81}\mathrm{Tl}^{208}$ on alpha decay.

If $M$ is atomic mass, $A$ is a mass number, What is meaning of  $\frac{\left(M-A\right)}{A}$?

Define magic numbers of nucleus of an atom.

The half-life of ${}^{40}\mathrm{K}$ is $1.28\times {10}^9 \mathrm{years}.$ What mass of this nuclide (in mg) has an activity of $1.00 \mathrm{\mu Ci}?$

(Given ${\mathrm{N}}_{\mathrm{A}}=6.023\times {10}^{23}$)

Report your answer up to two places of decimal.

$1{\mathrm{C}}_{\mathrm{i}}=$$3.7\times {10}^{10} \mathrm{dps}$

$1{\mathrm{C}}_{\mathrm{i}}=$_____$\times {10}^{10} \mathrm{Bq}$

The disintegration rate for a sample containing ${}_{27}{}^{60}\mathrm{Co}$ as the only radioactive nuclide, is found to be $240$ atoms/minute. ${\mathrm{t}}_{\frac{1}{2}}$ of $\mathrm{Co}$ is $5.2$ years. Find the number of atoms of $\mathrm{Co}$ in the sample. How long(in years) must this radioactive sample be maintained before the rate falls to $100$ disintegration per minute?

Calculate the weight (in $\mathrm{mg}$) of ${}^{14}\mathrm{C} \left({\mathrm{t}}_{1/2}=5720 \mathrm{yr}\right)$ atoms which will give $3.70\times {10}^7$ disintegration per second ($\mathrm{dps}$).

If $5 \mathrm{g}$ of a radioactive substance has ${\mathrm{t}}_{\frac{1}{2}}=14 \mathrm{h}, 20 \mathrm{g}$ of the same substance will have a ${\mathrm{t}}_{\frac{1}{2}}$ equal to

The rate of the process: $\mathrm{Cu}\to \mathrm{Ni}+{}_{+1}{}^0\mathrm{e}$

Radioactive disintegration rate is affected by

Half-life of a radioactive sample is $2\mathrm{x}$ years. What fraction of this sample will remain undecayed after $\mathrm{x}$ years?

Which of the following statements are correct?

Which of the following statements are correct?