The radioactivity of a uranium specimen with mass number 238 is 2.5×104s-1, the specimen's mass is 2 g. Find the half life.

N=2238×6.02×1023=5.06×1021Since R=λN⇒λ=RN=2.5×1045.06×1021=4.94×10-18 s-1 ⇒t1/2=0.693λ=1.4×1017 s

The radioactivity of a uranium specimen with mass number 238 is 2.5×104s-1, the specimen's mass is 2 g. Find the half life.

N=2238×6.02×1023=5.06×1021Since R=λN⇒λ=RN=2.5×1045.06×1021=4.94×10-18 s-1 ⇒t1/2=0.693λ=1.4×1017 s

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The radioactivity of a uranium specimen with mass number $238$ is $2.5 \times 10^{4} s^{- 1}$ , the specimen's mass is $2 g$ . Find the half life.

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$2.4 \times 10^{17} s$

$1.4 \times 10^{- 17} s$

$2.4 \times 10^{- 17} s$

$1.4 \times 10^{17} s$

answer is B.

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Detailed Solution

$N = \frac{2}{238} \times 6.02 \times 10^{23} = 5.06 \times 10^{21}$

Since $R = λ N$

$\Rightarrow λ = \frac{R}{N} = \frac{2.5 \times 10^{4}}{5.06 \times 10^{21}} = 4.94 \times 10^{- 18} s^{- 1} \Rightarrow t_{1 / 2} = \frac{0.693}{λ} = 1.4 \times 10^{17} s$

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The radioactivity of a uranium specimen with mass number 238 is 2.5×104s-1, the specimen's mass is 2 g. Find the half life.

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The radioactivity of a uranium specimen with mass number $238$ is $2.5 \times 10^{4} s^{- 1}$ , the specimen's mass is $2 g$ . Find the half life.