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The half-life of a radioactive substance is 48 hours. How much time will it take to disintegrate to its $\frac{1}{16}$ th part

12 h

16 h

48 h

192 h

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Explanation

(d) $\frac{N}{N_{0}} - {(\frac{1}{2})}^{t / T} \Rightarrow \frac{1}{16} = {(\frac{1}{2})}^{t / 48}$

$\Rightarrow {(\frac{1}{2})}^{4} = {(\frac{1}{2})}^{t / 48} \Rightarrow t = 192 hour$

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A radioactive substance has an average life of 5 hours. In a time of 5 hours

Half of the active nuclei decay

Less than half of the active nuclei decay

More than half of the active nuclei decay

All active nuclei decay

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Explanation

(c) If $λ$ is the decay constant of a radioactive substance than average life = $\frac{1}{λ}$
Also half life = $\frac{0.693}{λ} = 0.693 \times (A v e r a g e l i f e)$
in single average life, more than 63% of radioactive nuclei decay

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Which of the following radiations has the least wavelength

X-rays

$γ$ -rays

$β$ -rays

$α$ -rays

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Explanation

(b) $γ$ -rays have least wavelength.

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A radioactive sample at any instant has its disintegration rate 5000 disintegration per minute. After 5 minutes, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is

0.8 In 2

0.4 In 2

0.2 In 2

0.1 In 2

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Explanation

(b) $λ = \frac{\log_{e} \frac{A_{1}}{A_{2}}}{t} = \frac{\log_{e} \frac{5000}{1250}}{5} = 0.4 \ln 2$

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A nucleus with Z = 92 emits the following in a sequence:
$α, β^{-}, β^{-}, α, α, α, α, α, β^{-}, β^{-}, α, β^{+}, β^{+}, α$ . The Z of the resulting nucleus is

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Explanation

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Radioactive nuclei that are injected into a patient collect at certain sites within its body, undergoing radioactive decay and emitting electromagnetic radiation. These radiations can then be recorded by a detector. This procedure provides an important diagnostic tool called

Gamma camera

CAT scan

Radiotracer technique

Gamma ray spectroscopy

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Explanation

(c) Radioactive nuclei that are injected into a patient collected at certain sites within its body, undergoing radioactive decay and emitting electromagnetic radiation. These radiation can then be recorded by a detector. This procedure provides an important diagnostic tool called radio tracer technique.

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A radioactive decay chain starts from ${}_{93}^{237}{Np}$ and produces ${}_{90}^{229}{Th}$ by successive emissions. The emitted particles can be

Two $α$ -particles and one $β$ -particle

Three $β^{+}$ particles

One $α$ particle and two $β^{+}$ particles

One $α$ particle and two $β^{-}$ particles

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Explanation

(a) By using $n_{α} = \frac{A - A'}{4}$ and $n_{β} = 2 n_{α} - Z + Z'$

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The half-life of a sample of a radioactive substance is 1 hour. If $8 \times 10^{10}$ atoms are present at t = 0, then the number of atoms decayed in the duration t = 2 hour to t = 4 hour will be

$2 \times 10^{10}$

$1.5 \times 10^{10}$

Zero

Infinity

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Explanation

(b) $N = N_{0} {(\frac{1}{2})}^{\frac{t}{T_{1 / 2}}}$
No of atoms at t = 2hr, $N_{1} = 8 \times 10^{10} {(\frac{1}{2})}^{\frac{2}{1}} = 2 \times 10^{10}$
No. of atoms at t = 4hr, $N_{2} = 8 \times 10^{10} {(\frac{1}{2})}^{\frac{4}{1}} = \frac{1}{2} \times 10^{10}$
$∴$ No. of atoms decayed in given duration

$= (2 - \frac{1}{2}) \times 10^{10} = 1.5 \times 10^{10}$

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Carbon dating is best suited for determining the age of fossils if their age in years is of the order of

$10^{3}$

$10^{4}$

$10^{5}$

$10^{6}$

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Explanation

(b)

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A count rate meter shows a count of 240 per minute from a given radioactive source. One hour later the meter shows a count rate of 30 per minute. The half-life of the source is

120 min

80 min

30 min

20 min

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Explanation

(d) $A = A_{0} {(\frac{1}{2})}^{n} \Rightarrow 30 = 240 {(\frac{1}{2})}^{n} \Rightarrow {(\frac{1}{2})}^{3} = {(\frac{1}{2})}^{n} \Rightarrow n = 3$

$∴ \frac{t}{T_{1 / 2}} = 3 \Rightarrow T_{1 / 2} = \frac{t}{3} = \frac{1}{3} hr = 20 \min$

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