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Chapter 25: Problem 8

Just as the uranium series is called the "4n \(+2^{\prime \prime}\) series, the thorium series can be called the "4n" series and the actinium series the "4n \(+3 "\) series. A \(4 n+1 "\) series has also been established, with \(^{241} \mathrm{Pu}\) as the parent nuclide. To which series does each of the following belong: (a) \(\frac{214}{83} \mathrm{Bi} ;\) (b) \(\frac{216}{84} \mathrm{Po} ;\) (c) \(\frac{215}{85} \mathrm{At}\) (d) \(\frac{235}{92} \mathrm{U} ?\)

Short Answer

Expert verified
(a) 214/83 Bi does not belong to any series. (b) 216/84 Po belongs to the thorium (4n) series. (c) 215/85 At does not belong to any series. (d) 235/92 U does not belong to any series.

Step by step solution

01

Calculate 'n' for each isotope

The value of 'n' for each isotope can be calculated from the mass number using the equation \( n = \frac{A}{4} \), where 'A' is the mass number of the isotope.
02

Determine the decay series for 214/83 Bi

For the isotope Bi-214 (214/83 Bi), the mass number is 214. So \( n = \frac{214}{4} = 53.5 \). Since 'n' is not an integer, it does not belong to any of the specified series.
03

Determine the decay series for 216/84 Po

For the isotope Po-216 (216/84 Po), the mass number is 216. So \( n = \frac{216}{4} = 54 \). Since 'n' is an integer and 216 is a multiple of 4 ('4n' series), the isotope belongs to the thorium series.
04

Determine the decay series for 215/85 At

For the isotope At-215 (215/85 At), the mass number is 215. So \( n = \frac{215}{4} = 53.75 \). Since 'n' is not an integer, the isotope does not belong to any of the specified series.
05

Determine the decay series for 235/92 U

For the isotope U-235 (235/92 U), the mass number is 235. So \( n = \frac{235}{4} = 58.75 \). This doesn't fall into any of the specified series, since 'n' is not an integer.

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Most popular questions from this chapter

Write equations for the following nuclear reactions. (a) bombardment of \(^{7} \mathrm{Li}\) with protons to produce \(^{8} \mathrm{Be}\) and \(\gamma\) rays (b) bombardment of \(^{9} \mathrm{B}\) with \(_{1}^{2} \mathrm{H}\) to produce \(^{10} \mathrm{B}\) (c) bombardment of \(^{14} \mathrm{N}\) with neutrons to produce \(^{14} \mathrm{C}\)

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