Let $N_{\beta}$ be the number of $\beta $ particles emitted by $1$ gram of $Na^{24}$ radioactive nucler (half life $= 15\, hrs$) in $7.5\, hours$, $N_{\beta}$ is close to (Avogadro number $= 6.023\times10^{23}\,/g.\, mole$)

The half life of the isotope $_{11}N{a^{24}}$ is $15 \,hrs$. How much time does it take for $\frac{7}{8}th$ of a sample of this isotope to decay.........$hrs$

Which of the following statements are true regarding radioactivity

$(I)$ All radioactive elements decay exponentially with time

$(II)$ Half life time of a radioactive element is time required for one half of the radioactive atoms to disintegrate

$(III)$ Age of earth can be determined with the help of radioactive dating

$(IV)$ Half life time of a radioactive element is $50\%$ of its average life periodSelect correct answer using the codes given belowCodes :

Define the disintegration rate or radioactivity of a sample and obtain the relation $R = \lambda N$ and define its different units. 

Give the equation form of exponential law. 

In a radioactive material the activity at time $t_1$ is $R_1$ and at a later time $t_2$ it is $R_2$. If the decay constant of the material is $\lambda$ then