CBSE Class 12 · 2006 · All India · Modern PhysicsShort Answer

Define the terms half-life period and decay constant of a radioactive substance. Write their S.I. units. Establish the relationship between the two.

Answer: $T_{1/2}$ (s), $λ$ (s $^{- 1}$ ); $T_{1/2} = 0.693/ λ$ .

Solution

Half-life

T_{1/2}

: time for the number of undecayed nuclei to reduce to half; S.I. unit second (s).
Decay constant

λ

: the fraction of nuclei decaying per unit time; S.I. unit s

^{- 1}

.
From

N = N_{0} e^{- λ t}

, at

t = T_{1/2}

N = N_{0} /2

\frac{1}{2} = e^{- λ T_{1/2}} \Rightarrow λ T_{1/2} = ln 2.

T_{1/2} = \frac{0.693}{λ}

CBSE Class 12 Board · 2006 · All India · Subjective