The half-life of 92 238 U against α − decay is 4.5 × 10 9 years. Calculate the activity of 1 g sample of 92 238 U .

T 1 2 = 4.5 × 10 9 years = 4 .5 × 10 9 × 3 .156 × 10 7 s No. of atoms in 1 g Uranium, N = 6.023 × 10 23 238 atomsThe activity of the sample = λ N = 0.693 T 1 2 × N = 0.693 × 6.023 × 10 23 4.5 × 3.156 × 10 16 × 238 = 1.235 × 10 4 distintegration/second .

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PhysicsModern PhysicsRadioactivityEasy2 minPYQ_2020

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The half-life of $_{92}^{238} U$ against $α -$ decay is $4.5 \times 10^{9}$ years. Calculate the activity of $1 g$ sample of $_{92}^{238} U$ .

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Solution:

$T_{\frac{1}{2}} = 4.5 \times 10^{9}$ years $= 4 .5 \times 10^{9} \times 3 .156 \times 10^{7} s$ No. of atoms in $1 g$ Uranium, $N = \frac{6.023 \times 10^{23}}{238}$ atomsThe activity of the sample $= λ N$ $= \frac{0.693}{T_{\frac{1}{2}}} \times N$ $= \frac{0.693 \times 6.023 \times 10^{23}}{4.5 \times 3.156 \times 10^{16} \times 238}$ $= 1.235 \times 10^{4} distintegration/second .$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Modern PhysicsSubtopic:Radioactivity

⏱ 2mℹ️ Source: PYQ_2020

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