The half-life of $^{60}Co$ is $7 \ years$. If $1 \ g$ of it decays,the amount of the substance remaining after $28 \ years$ is (in $g$)

$A$ radioactive element gets spilled over the floor of a room. Its half-life period is $30$ days. If the initial activity is ten times the permissible value,after how many days will it be safe to enter the room?

The half-life period of radioactive decay of ${}^{14}C$ is $5730 \ years$. An archaeological artifact contains $80\%$ of ${}^{14}C$ as compared to a living tree. Calculate the age of the sample in $years$.

The disintegration constant for a radioactive substance is $0.58 \, hr^{-1}$. Its half-life period is $........ \, hr$.

$A$ freshly prepared radioactive source of half-life $2 \ hours$ emits radiations of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with this source is ......... $hours$.

The number of $\alpha$-particles emitted per second by a radioactive element falls to $1/32$ of its original value in $50 \ days$. The half-life period of this element is .......... $days$.