The number of undecayed nuclei in the radioactive sample decays exponentially with time.

A rate of decay of a radioactive element is independent of temperature, pressure, Infact for any external conditions. A simple law discovered by Rutherford states that a certain fraction of any sample of radioactive element undergoes change in a unit time. If we start with  10mg   of the radioactive substance  (t1/2  =  1day)  , only  5mg will be left at the end of the first day. At the end of 2nd day  2.5mg will be left and so on. λ  =  2.303tlogaa − x A radioactive element has atomic mass 90 amu and a half – life of 28 years. The number of disintegrations per second per gm of the element is

The isotope carbon-14, 614 𝐶𝐶, is radioactive and has a half-life of 5 730 years. If you start with a sample of 1 000 carbon-14nuclei, how many nuclei will still be undecayed in 25 000 years?

Consider a radioactive sample whose decay constant is λ. Initial (t=0) number of nuclei is N0. Find the total life of all the nuclei that decay in the interval of second and third half-lives (i.e.t=t1/2 to t=3t1/2)

Derive an expression that relates the half-life and the decay constant for a sample of aparticular radioactive nucleus. Calculate the half-life and decay constant for a radioactiveisotope sample if the initial number of radioactive atoms is 450 and this reduces to 63 after24.3 hours.

Which of the following is NOT equal to the half-life of an isotope?Half the time it takes for all of the radioactive nuclei present in a sample to decayThe time it takes for the number of nuclei in a sample of the isotope to halveThe time it takes for the count rate from a sample of the isotope to fall to 50% of its initial valueThe time it takes for the activity of a sample of the isotope to fall to half of its initial level2Which of the following equations links the total count rate from a source, its corrected count rate, and the background count rate?Background count rate = total count rate + corrected count rateTotal count rate = corrected count rate – background count rateCorrected count rate = total count rate – background count rateCorrected count rate = total count rate + background count rate3There are initially 400,000 nuclei present in a sample of radioactive material of half-life 30 minutes.  How many of these nuclei will remain after two hours?100,00050,000200,00025,0004Carbon-11 has a half-life of approximately 20 minutes.  The corrected count rate at a given point in time from a sample of carbon-11 is 160 counts per second.  What would the corrected count rate from the sample have been 40 minutes earlier?320 counts per second80 counts per second40 counts per second640 counts per second5A GM tube is connected to a rate meter.  With no source present, the reading on the rate meter is 12 counts per second.  When a source is brought close to the GM tube, the reading increases to 60 counts per second.  Calculate the corrected count rate from the source.5 counts per second48 counts per second12 counts per second72 counts per second