Physics · nuclei · NEET
No, they are opposite in feel but linked. Half-life is the TIME for half the nuclei to decay. Decay constant lambda is a PROBABILITY per second. They are connected by T(1/2) = 0.693 / lambda. A large lambda gives a small half-life (fast decay), a small lambda gives a large half-life (slow decay).
The unit is per second (s^-1), or more generally inverse time (per minute, per year, etc). This is because lambda tells you the fraction of nuclei that decay in one unit of time. It has no mass or charge unit, only 1/time.
No. Lambda is a fixed property of a given nucleus. Radioactive decay comes from inside the nucleus, so it is not affected by outside things like temperature, pressure, chemical state, or how much sample you have. Two grams and one gram of the same isotope have the exact same lambda.
Activity R is the number of decays happening each second, given by R = lambda N. Decay constant lambda is only the per-nucleus probability. So activity depends on both lambda AND how many nuclei N are left. As N falls with time, activity falls, but lambda stays constant.
The minus sign shows that the number of nuclei is DECREASING with time. The rate of decay is dN/dt = -lambda N. The negative sign means N goes down as t increases. When you solve this equation you get N = N0 e^(-lambda t), where N0 is the starting number.
Mean life (tau) is the average time a nucleus survives before decaying. It equals tau = 1 / lambda. So mean life is simply the reciprocal of the decay constant. Also, half-life T(1/2) = 0.693 x tau = 0.693 / lambda.
It is the chance that a single nucleus will break apart (decay) in one second. A higher value means the nucleus decays sooner.
From the decay law, lambda = -(1/N)(dN/dt). It also connects to half-life as lambda = 0.693 / T(1/2), and to mean life as lambda = 1 / tau.
Per second (s^-1). It is inverse time because it represents a fraction decaying per unit time.
For a stable nucleus effectively yes (it does not decay). For any radioactive nucleus lambda is always positive and fixed for that isotope.
A high decay constant decays faster and has a shorter half-life. A low decay constant decays slowly with a long half-life.
