CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The half life period of a radioactive element $$X$$ is same as the mean life time of another radioactive element $$Y$$. Initially they have the same number of atoms. Then


A
X and Y decay the same rate always
loader
B
X will decay faster than Y
loader
C
Y will decay faster than X
loader
D
X and Y have same decay rate initially
loader

Solution

The correct option is C $$X$$ will decay faster than $$Y$$
Let the number of atoms of X and Y presented initially be $$N_o$$.
Number of atoms of X remaining after time $$t$$ is given by  $$N_X = N_o e^{-\lambda t}$$
$$N_X = N_oe^{ -\frac{\ln 2 t}{T_{1/2}}} = N_o e^{ - \frac{\ln 2 t}{T_m}}$$     ($$\because T_{1/2} = T_m$$)
where and $$T_{1/2}$$ is the half-time of $$X$$ ans $$T_m$$ is the mean life time of $$Y$$.
Number of atoms of Y remaining after time $$t$$ is given by  $$N_Y = N_o e^{-\lambda t} = N_o e^{-\frac{t}{T_m}}$$
$$\implies$$  $$N_X<N_Y$$  at any time $$t$$
Thus, $$X$$ decays faster than $$Y$$.

Physics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image