Periodo de semidesintegración

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**Evolución de una muestra**
Periodos de semidesin- tegración transcurridos	Núcleos sin desintegrar
0	100 % (todos)
1	50 % (1 de cada 2)
2	25 % (1 de cada 4)
3	12,5 % (1 de cada 8)
4	6,25 % (1 de cada 16)
5	3,125 % (1 de cada 32)
6	1,562 5 % (1 de cada 64)
7	0,781 25 % (1 de cada 128)
N	${\frac {100}{2^{N}}}\%$ (1 de cada 2^N)

En física nuclear y radioquímica se define el período de semidesintegración o constante de semidesintegración, también llamado semivida o hemivida, como el tiempo necesario para que se desintegren la mitad de los núcleos de una muestra inicial de un radioisótopo. Se toma como referencia la mitad de ellos debido al carácter aleatorio de la desintegración nuclear.

El período de semidesintegración no debe confundirse con la vida media. Este concepto es ampliamente utilizado en los cálculos de cinéticas nucleares, para poder caracterizar los nuclidos, como también como un patrón de pureza nuclear de las muestras. Esta constante suele representarse con $\tau$ .

También se puede entender como el tiempo que tardan en transmutarse la mitad de los átomos radiactivos de una muestra. Un ejemplo es el carbono-14 utilizado para datar restos orgánicos antiguos.

Notación:

$t_{1/2}$ es el período de semidesintegración.
$N(t)$ es el número de núcleos de la muestra en el instante tiempo t.
$N_{0}$ es el número inicial (cuando t = 0) de núcleos de la muestra.
$\lambda$ es la constante de desintegración.

El instante en el que el número de núcleos se ha reducido a la mitad es $t_{1/2}\,$ . O sea:

N(t_{1/2})=N_{0}\cdot {\frac {1}{2}}

Sustituyendo en la fórmula de decaimiento exponencial:

N_{0}\cdot {\frac {1}{2}}=N_{0}e^{-\lambda t_{1/2}}\,

e^{-\lambda t_{1/2}}={\frac {1}{2}}\,

-\lambda t_{1/2}=\ln {\frac {1}{2}}=-\ln {2}\,

Por tanto, la relación entre el período de semidesintegración de un radioisótopo ( $t_{1/2}$ ) y su constante de desintegración ( ${\lambda }$ ) es:

t_{1/2}={\frac {\ln 2}{\lambda }}\,

Y como su vida media ( $\tau$ ) es

\tau ={\frac {1}{\lambda }}

resulta que el período de semidesintegración es aproximadamente el 69,31 % de su vida media.

Si queremos calcular el tiempo que tarda una muestra de un radioisótopo en reducirse al 20 % de la inicial haremos:

$Co$ = Concentración inicial.

$Ct=0.2*Co$

$K$ = Constante de semidesintegración

$t_{1/2}$ = Periodo de semidesintegración

$t_{1/2}={\frac {\ln({\frac {Co}{Ct}})}{k}}$

La velocidad de desintegración de un contaminante será menor cuanto menos cantidad de contaminante quede (suponemos que el contaminante sigue una cinética de primer orden).

Periodos de semidesintegración de algunos radionucleidos

Uranio-235	7,038·10⁸ años	Uranio-238	4,468·10⁹ años	Potasio-40	1,28·10⁹ años
Rubidio-87	4,88·10¹⁰ años	Calcio-41	1,03·10⁵ años	Carbono-14	5760 años
Radio-226	1600 años	Cesio-137	30,07 años	Bismuto-207	31,55 años
Estroncio-90	28,90 años	Cobalto-60	5,27 años	Cadmio-109	462,6 días
Yodo-131	8,02 días	Radón-222	3,82 días	Oxígeno-15	122 segundos

Véase también

Datos: Q98118544

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