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प्रश्न
The mean lives of a radioactive substance are 1620 and 405 years for β-emission and β-emission respectively. The time after which three fourth of a sample will decay if it is decaying both by β-emission and β-emission simultaneously will be ______ years.
(Take ln 2 = 0.693)
विकल्प
440
449
450
400
MCQ
रिक्त स्थान भरें
उत्तर
The mean lives of a radioactive substance are 1620 and 405 years for β-emission and β-emission respectively. The time after which three fourth of a sample will decay if it is decaying both by β-emission and β-emission simultaneously will be 449 years.
Explanation:
`1/T = 1/T_alpha + 1/T_beta`
⇒ T = `(T_alphaT_beta)/(T_alpha + T_beta)` = 324 years
`N/N_0 = e^{-lambdat}`
`t = 1/lambda ℓn N_0/N = T ℓn N_0/N`
t = 324 × 2ℓn2
t = 449.06 years
t ≈ 449 years
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