$A$ piece of wood was found to have the $C^{14}/C^{12}$ ratio $0.7$ times that in a living plant. The time period when the plant died is ....... $years$ (Half-life of $C^{14} = 5760 \, yrs$).

$A$ radioactive substance has a constant activity of $2000$ disintegrations/minute. The material is separated into two fractions,one of which has an initial activity of $1000$ disintegrations per minute while the other fraction decays with $t_{1/2} = 24 \ h$. The total activity in both samples after $48 \ h$ of separation is

$A$ wood piece is $11460$ years old. What is the fraction of $^{14}C$ activity left in the piece? (Half-life period of $^{14}C$ is $5730$ years)

In the case of a radioisotope,the value of $T_{1/2}$ and $\lambda$ are identical in magnitude. The value is

The half-life of a radioactive element is $100 \, \text{min}$. The time interval between the stages of $50\%$ and $87.5\%$ decay will be ...... $\text{min}$.

$A$ radioactive sample is emitting $64$ times more radiation than the non-hazardous limit. If its half-life is $2 \ hr$,after what time will it become non-hazardous? $(hr)$