$C^{14}$ has a half-life of $5700$ years. At the end of $11400$ years,the actual amount left is:

The half-life of a radioactive substance is $30 \text{ minutes}$. The time taken between $40 \%$ decay and $85 \%$ decay of the same radioactive substance is

Half-life of a radioactive element depends upon:

An accident in a nuclear laboratory resulted in the deposition of a certain amount of radioactive material with a half-life of $18$ days inside the laboratory. Tests revealed that the radiation level was $64$ times higher than the permissible level required for safe operation. What is the minimum number of days after which the laboratory can be considered safe for use?

At any instant,the ratio of the amount of two radioactive substances is $2 : 1$. If their half-lives are $12$ hours and $16$ hours respectively,what will be the ratio of the substances after two days?

$A$ radioactive source has a half-life of $6 \,h$. $A$ freshly prepared sample of the same exhibits radioactivity $32$ times the permissible safe value. The minimum time after which it would be possible to work safely with the source is (in $\,h$)