A certain radioactive nuclide of mass number $m_x$ disintegrates, with the emission of an electron and $\gamma$ radiation only, to give second nuclied of mass number $m_y.$ Which one of the following equation correctly relates $m_x$ and $m_y$ ?

Half life of radium is $1620$ years. How many radium nuclei decay in $5$ hours in $5\, gm$ radium? ( Atomic weight of radium $= 223$)

$16\, gm$ sample of a radioactive element is taken from Bombay to Delhi in $2\, hour$ and it was found that $1\, gm$ of the element remained (undisintegrated). Half life of the element is

A fraction $f_1$ of a radioactive sample decays in one mean life, and a fraction $f_2$ decays in one half-life.

A solution containing active cobalt ${}_{27}^{60}Co$ having activity of $0.8\,\mu Ci$ and decay constant $\lambda $ is injected in an animal's body. If $1 \,cm^3$ of blood is drawn from the animal's body after $10\, hrs$ of injection, the activity found was $300\, decays$ per minute. What is the volume of blood that is flowing in the body?……….$litres$ ( $ICi = 3.7 \times 10^{10}$ decay per second and at $t = 10\, hrs$ ${e^{ – \lambda t}} = 0.84$ )