Question 618: Atoms & Nuclei

Question

A radioactive element $$X$$ convents into another stable element $$Y$$. Half-life of $$X$$ is 2 hrs. Initially only $$X$$ is present. After time $$t$$, the ratio of atoms of $$X$$ and $$Y$$ is found to be $$1: 4$$, then $$t$$ in hours is

Accepted Answer

Let $$N_0=N_0$$ of atoms of $$X$$ at time $$t=0$$.
At $$t=4$$ hrs (two half lives)
$$N_x=\frac{N_0}{4} 	ext { and } N_y=\frac{3 N_0}{4} \Rightarrow N_x / N_y=1 / 3$$
At $$t=6$$ hrs (three half lives)
$$N_x=\frac{N_0}{8} 	ext { and } N_y=\frac{7 N_0}{8}, \frac{N_x}{N_y}=\frac{1}{7}$$
The given ratio $$1 / 4$$ lies between $$1 / 3$$ and $$1 / 7$$. Therefore, $$t$$ lies between 4 hrs and 6 hrs.

Answer

2

Answer

4

Answer

between 4 and 6

Answer

6

Atoms & Nuclei

A radioactive element $X convents into another stable element Y. Half-life of X is 2 hrs. Initially only X is present. After time t, the ratio of atoms of X and Y is found to be 1: 4, then t$ in hours is

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