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Question: A\[Li\] target is bombarded with a proton beam current of\[{10^{ - 4}}\]\[A\] for one hour to produc...

ALiLi target is bombarded with a proton beam current of{10^{ - 4}}$$$$A for one hour to produce BeBe of activity 1.8×108dps1.8 \times {10^8}dps. Assuming that one BeBe radioactive nuclei is produced by bombarding 10001000 protons, its half-life is:
(a) 0.87 \times {10^7}$$$$s
(b) 0.2 \times {10^7}$$$$s
(c) 0.67 \times {10^8}$$$$s
(d) 0.87 \times {10^6}$$$$s

Explanation

Solution

Atomic number – Atomic number is the number of protons in the nucleus of an atom.
Atomic number of lithium (LiLi) =33
Atomic number of beryllium (BeBe) = 4
A nucleus consists of protons, electrons and neutrons.
Protons – protons are a type of subatomic particle with positive charge.
Electrons – Electrons are a type of subatomic particles with negative charge.
Neutrons – Neutrons are subatomic particles with no charge.

Complete step by step answer:
Given that, current (I)\left( I \right)=104A{10^{ - 4}}A, Time(t)\left( t \right)= 1h1h=3600s3600s
We also know that
Q=ItQ = It
Where, QQis electric charge, II is electric current and tt is time.
Q=104×1×3600Q = {10^{ - 4}} \times 1 \times 3600=0.36C0.36C
Number of protons = Qe\dfrac{Q}{e} = 0.361.6×1019\dfrac{{0.36}}{{1.6 \times {{10}^{ - 19}}}}
Number of protons =2.25×1082.25 \times {10^8}
Produced number of BeBe nuclei = 2.25×10181000\dfrac{{2.25 \times {{10}^{18}}}}{{1000}}
= 2.25×10152.25 \times {10^{15}}
Given that, activity of BeBe = 1.8×108dps1.8 \times {10^8}dps
∴ Activity =λN\lambda N
Activity= ln2t1/2N\dfrac{{\ln 2}}{{{t_{1/2}}}}N
λ=ln2t1/2\lambda = \dfrac{{\ln 2}}{{{t_{1/2}}}}
Given that, value of activity = 1.8×108dps1.8 \times {10^8}dps
1.8×108=0.693t1/2×2.25×10151.8 \times {10^8} = \dfrac{{0.693}}{{{t_{1/2}}}} \times 2.25 \times {10^{15}}
Then,
t1/2=0.693×2.25×10151.8×108{t_{1/2}} = \dfrac{{0.693 \times 2.25 \times {{10}^{15}}}}{{1.8 \times {{10}^8}}}
t1/2=0.87×107s{t_{1/2}} = 0.87 \times {10^7}s

So, the correct answer is “Option A”.

Note:
Radioactive decay – Radioactive decay is the process by which an unstable atomic nucleus loses energy by radiations. When an unstable atom gets radioactive then the number of protons change in the nucleus. Radioactive sources are used to treat diseases, to produce energy, to sterilize instruments. Sometimes nucleus breaks, undergoing nuclear decay. All elements with 84 or more protons are unstable and undergo decay.