SATHEE: Atoms And Nuclei Question 403

Atoms And Nuclei Question 403

Question: A $^{7} L i$ target is bombarded with a proton beam current of $10^{- 4}$ A for 1 hour to produce $^{7} B e$ of activity $1.8 \times 10^{8}$ disintegrations per second. Assuming that one $^{7} B e$ radioactive nucleus is produced by bombarding 1000 protons, determine its half-life.

Options:

A) $8.6 \times 10^{6} s$

B) $4.2 \times 10^{5} s$

C) $3.1 \times 10^{5} s$

D) $1.1 \times 10^{6} s$

Show Answer

Answer:

Correct Answer: A

Solution:

The total number of protons bombarded

$= \frac{i t}{λ} = \frac{10^{- 4} \times 3600}{1.6 \times 10^{- 19}} = 22.5 \times 10^{17}$

Number of $^{7} B e$ produced $N = \frac{22.5 \times 10^{17}}{1000} = 22.5 \times 10^{14}$

We know that activity $A = λ N$ or $A = (\frac{0.693}{t_{1 / 2}}) N$
$∴, t_{1 / 2} = 0.693 \frac{N}{A} = 0.693 \times \frac{22.5 \times 10^{14}}{1.8 \times 10^{8}}$ $= 8.63 \times 10^{6} s$

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Atoms And Nuclei Question 403

Question: A 7Li target is bombarded with a proton beam current of 10−4 A for 1 hour to produce 7Be of activity 1.8×108 disintegrations per second. Assuming that one 7Be radioactive nucleus is produced by bombarding 1000 protons, determine its half-life.

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Question: A $^{7} L i$ target is bombarded with a proton beam current of $10^{- 4}$ A for 1 hour to produce $^{7} B e$ of activity $1.8 \times 10^{8}$ disintegrations per second. Assuming that one $^{7} B e$ radioactive nucleus is produced by bombarding 1000 protons, determine its half-life.