Question

The most radioactive of the isotope of an element is the one with the largest value of its:
(a)- half-life
(b)- neutron number
(c)- atomic number
(d)- decay constant

Answer 1

Hint: The most radioactive metal is related to its radioactive decay constant. The most radioactive isotope will take the least time to disintegrate.

Complete answer:
Let us first understand radioactivity:
Radioactivity: radioactivity is the phenomenon of spontaneous disintegration of the nucleus of an atom with the emission of one or more penetrating radiations like \[\alpha -particles\], \[\beta -particles\] \[\text{or }\gamma -particles\]
A naturally occurring heavy nucleus is unstable. It spontaneously emits a particle, without the stimulus of any outside agency, transforming itself into a different nucleus. Such a nucleus is said to be radioactive and the process of transformation is radioactive decay. The process is spontaneous in the sense that it occurs by itself. It cannot be initiated, stopped, accelerated, or retarded by changing.
(a)- chemical condition or
(b)- physical conditions like temperature, pressure, etc. other than the nuclear bombardment.
Experimentally the number of active nuclei in a radioactive sample decreases exponentially with time. The disintegration is fast in the beginning but becomes slower and slower with the passage of time.
The larger the value of the decay constant, the higher is the rate of disintegration.
The radioactive decay constant may be defined as the ratio of the instantaneous rate of disintegration to the number of active nuclei present in the radioactive sample.
$\lambda =\dfrac{-\dfrac{dN}{dt}}{N}$
Where, $-\dfrac{dN}{dt}$ is the rate of disintegration and N is the number of active nuclei present.

Hence, the correct answer is an option (d)- decay constant.

Note: Irrespective of its nature, a radioactive sample will take an infinitely long time to disintegrate completely. The radioactive decay constant is directly proportional to the number of undecayed nuclei present in the sample.