A radioactive substance has a half life of `t_(0)`. Two particular nuclei let's name them as nucleus A and B - have not decayed over a particular observation period of `6t_(0)` The probability that both A and B will survive over a further period of `3t_(0)` is `(y)/(8z)` Find y+z (y and z are least possible integral values)
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A particular nucleus in a large population of identical radioactive nuclei did survive 5 halt lives of that isotope. Then the probability that this surviving nucleus will service the next half life is

Two radioactive substances have half-lives T and 2T. Initially, they have equal number of nuclei. After time t=4T , the ratio of their number of nuclei is x and the ratio of their activity is y. Then,

A radioactive nucleus A with a half life T, decays into nucleus B. At t=0, there is no nucleus B. At some time t, the ratio of the number of B to that of A is 0.3 . Then, t is given by

A radioactive substance has a half-life of 64.8 h. A sample containing this isotope has an initial activity (t=0) of 40muCi . Calculate the number of nuclei that decay in the time interval between t_1=10.0h and t_2=12.0h .

The half life of a radioactive substance is T_(0) . At t=0 ,the number of active nuclei are N_(0) . Select the correct alternative.

Find x ,\ y and z so that A=B , where A=[x-2 3 2z 18 z y+2 6z] , B=[y z6 6y x2y]

A radioactive substance "A" having N_(0) active nuclei at t=0 , decays to another radioactive substance "B" with decay constant lambda_(1) . B further decays to a stable substance "C" with decay constant lambda_(2) . (a) Find the number of nuclei of A, B and C time t . (b) What should be the answer of part (a) if lambda_(1) gt gt lambda_(2) and lambda_(1) lt lt lambda_(2)

Nuclei X and Y convert into a stable nucleus Z. At t=0 , the number of nuclei of X is 8 times that of Y. Half life of X is 1 hour and half life of y=2 hour. Find the time (in hour) at which rate of disintegration of X and Y are equal.

At a given, t = 0, two radioactive substances A and B have equal activities. The ratio (R_(B))/(R_(A)) of their activities after time t itself decays with time t as e^(-3t) , If the half-life of A is ln2, the half-life of B is :

Two radio active nuclei X and Y decay into stable nucleus Z X to Z + 2alpha+ beta^- Y to Z + alpha + 2 beta^+ if Z_1 and Z_2 are atomic numbers of X and Y then