Verified Solution • 2025–26 Session moderate

QPages 442-444: Q42: HC Verma: Concepts of Physics - Volume 2 The Nucleus Pages 442-444: Q42 Solution: can disintegrate either by emitting an -particle of by emitting …

83212Bi^{212}_{83}\text{Bi} can disintegrate either by emitting an α\alpha-particle of by emitting a β−\beta^--particle. a) Write the two equations showing the products of the decays. b) The probabilities of disintegration α\alpha- and β\beta-decays are in the ratio 7/13. The overall half-life of 212Bi^{212}\text{Bi} is one hour. If 1 g of pure 212Bi^{212}\text{Bi} is taken at 12.00 noon, what will be the composition of this sample at 1 P.m. the same day?

Step-by-Step Verified Solution

**Answer:** (a) _-decay: ___Bi _ ___Tl + _; __-decay: ___Bi _ ___Po + e_ + __. (b) Composition: 0.35 g Bi, 0.65 g Po/Tl mixture. **Step-by-Step Explanation:** (a) ___Bi (Z=83) can undergo: - _-decay: ___Bi _ ___Tl (Z=81) + _He. - __-decay: ___Bi _ ___Po (Z=84) + e_ + __. (b) Half-life = 1 h. After 1 h, half the nuclei decay. Probability of _-decay = 7/20, _-decay = 13/20. Mass of Bi remaining = 0.5 g. Mass of Tl (from _-decay) = 0.5 _ (7/20) _ (208/212) = 0.172 g. Mass of Po (from _-decay) = 0.5 _ (13/20) _ (212/212) = 0.325 g. Composition: 0.5 g Bi, 0.172 g Tl, 0.325 g Po[citation:2].

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