Radioactive decay

Explain the calculation of decay constant by graphical method.

Derive the expression of half life period of radioactive substances.

Discuss the law of radioactive disintegration.

Drive an expression for radioactive decay constant.

$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?

For two different disintegration half-lives are equal at equilibrium. This is possible when

One becquerel of radioactivity is equal to

STATEMENT-1: Specific activity of the same radioactive substance is same for 10g radioactive substance as well as 50g radioactive substance.

STATEMENT-2: Specific activity of a radioactive substance is its activity per g.

The mean lives of a radioactive substance are 1620 year and 405 year for -emission and $\mathrm{\beta }$ -emission respectively. Find the time during which three-fourth of a sample will decay if it is decaying both by

-emission and $\mathrm{\beta }$ -emission simultaneously.

Assertion: Unit of decay constant is ${\mathrm{s}\mathrm{e}\mathrm{c}}^{-1}$ .

Reason: Decay constant represents rate of disintegration.

Calculate the age of the ore if    ${}_{92}{\text{U}}^{238}$ by successive decay changes to ${}_{82}{\text{Pb}}^{206}$, when a sample of uranium ore was analysed it was found that it contains 1g of U²³⁸ and 0.1 g of Pb²⁰⁶, considering that all the Pb²⁰⁶ had accumulated due to decay of U²³⁸   (Half-life of U²³⁸ = 4.5 × 10⁹ yrs).