Advertisements
Advertisements
Question
A radioactive substance disintegrates into two types of daughter nuclei, one type with disintegration constant λ1 and the other type with disintegration constant λ2 . Determine the half-life of the radioactive substance.
Advertisements
Solution
\[\ce{X ->[\lambda_{1}]D_1}\]
\[\ce{X ->[\lambda_{2}]D_2}\]
`lambda_"effective" = lambda_1 + lambda_2`
half life `(t_(1/2)) = ("In" 2)/(lambda_"effective") = (0.693)/(lambda_1+lambda_2`
APPEARS IN
RELATED QUESTIONS
(a) Write the basic nuclear process involved in the emission of β+ in a symbolic form, by a radioactive nucleus.
(b) In the reactions given below:
(i)`""_16^11C->_y^zB+x+v`
(ii)`""_6^12C+_6^12C->_a^20 Ne + _b^c He`
Find the values of x, y, and z and a, b and c.
How is the mean life of a given radioactive nucleus related to the decay constant?
Under certain circumstances, a nucleus can decay by emitting a particle more massive than an α-particle. Consider the following decay processes:
\[\ce{^223_88Ra -> ^209_82Pb + ^14_6C}\]
\[\ce{^223_88 Ra -> ^219_86 Rn + ^4_2He}\]
Calculate the Q-values for these decays and determine that both are energetically allowed.
Why is it experimentally found difficult to detect neutrinos in this process ?
A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t1/2. Show that after a time t >> t1/2 the number of active nuclei will become constant. Find the value of this constant.
Disintegration rate of a sample is 1010 per hour at 20 hours from the start. It reduces to 6.3 x 109 per hour after 30 hours. Calculate its half-life and the initial number of radioactive atoms in the sample.
'Half-life' of a radioactive substance accounts for ______.
The half-life of a radioactive sample undergoing `alpha` - decay is 1.4 x 1017 s. If the number of nuclei in the sample is 2.0 x 1021, the activity of the sample is nearly ____________.
Draw a graph showing the variation of decay rate with number of active nuclei.
The activity R of an unknown radioactive nuclide is measured at hourly intervals. The results found are tabulated as follows:
| t (h) | 0 | 1 | 2 | 3 | 4 |
| R (MBq) | 100 | 35.36 | 12.51 | 4.42 | 1.56 |
- Plot the graph of R versus t and calculate the half-life from the graph.
- Plot the graph of ln `(R/R_0)` versus t and obtain the value of half-life from the graph.
