-212-83 Bi can disintegrate either by emitting an - -particle or- by emitting a - -particle- -a- Write the two equations showing the products of the decays- -b- The probabilities of disintegration by - - and - -decays are in the ratio 7-13- The overall half-life of -212 Bi is one hour- If 1 g of pure -212 Bi is taken at 12-00 noon- what will be the composition of this sample at 1 p-m- the same day- -

_83^212Bi → _91^289T1+_4^2He (α ) _83^212Bi → _64^289Bi+_4^2P_0 + e t_1/2 = 1 h, Time elapsed = 1 h At t = 0, ^212BiPresent = 1 g ∴ At t = 1, ^212 BiPresent = ...

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Byju's Answer

Standard XII

Physics

Alpha Decay

^212_83 Bi ca...

Question

$_{83}^{212}$ Bi can disintegrate either by emitting an $α$ -particle or
by emitting a $β^{-}$ -particle. (a) Write the two equations showing the products of the decays. (b) The probabilities of disintegration by $α$ - and $β$ -decays are in the ratio $\frac{7}{13}$ . The overall half-life of $^{212}$ Bi is one hour. If 1 g of pure $^{212}$ Bi is taken at 12.00 noon, what will be the composition of this sample at 1 p.m. the same day?

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Solution

$_{83}^{212} B i \to_{91}^{289} T 1 +_{4}^{2} H e (α)$

$_{83}^{212} B i \to_{64}^{289} B i +_{4}^{2} P_{0} + e$

$t_{\frac{1}{2}}$ = 1 h, Time elapsed = 1 h

At t = 0, $^{212}$ BiPresent = 1 g
$∴$ At t = 1, $^{212}$ BiPresent = 0.5 g

Probability $α$ -decay and $β$ -decay are in ratio $\frac{7}{13}$

$∴ \frac{T}{remained}$ = 0.175 g

$∴ P_{0}$ remained = 0.325 g.

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21283Bi→28991T1+24He(α) 21283Bi→28964Bi+24P0+e t12 = 1 h, Time elapsed = 1 h At t = 0, 212BiPresent = 1 g ∴ At t = 1, 212 BiPresent = 0.5 g Probability α -decay and β -decay are in ratio 713 ∴Tremained = 0.175 g ∴P0 remained = 0.325 g.