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Chapter 42: Q.48 (page 1237)

A 1 Ci source of radiation is a significant source. 238 U is an alpha emitter. What mass of 238 U has an activity of 1 Ci?

Short Answer

Expert verified

the mass of uranium is 2.96x10³kg

Step by step solution

01

Step 1

Number of atom is,

Here R₀ is initial and r is final decay rate

r = \frac{In 2}{t_{\frac{1}{2}}} Here t_{\frac{1}{2}} is half - life

02

Step 2

Convert Ci to Bq

1 C i = 3.7 x 10^{10} B q

So,

And final decay rate is calculated

Substitute 4.47x10⁹ year for t_1/2 from Appendix C in above final rate equation

$r = \frac{I n 2}{4.47 x 10^{9} y e a r} = (1.55 x 10^{- 10} d e c a y / y e a r) (\frac{1 y e a r}{31536 x 10^{3} s}) = 4.92 x 10^{- 18} d e c a y / s$

03

Step 3

Then the number of atom is calculated as follows

Substitute 3.7x10¹⁰ decay/sec for R₀ and 4.92x10^-18 decays for r in above eqution

$N_{0} = 7.5 x 10^{27} atoms Then the mass of 7.5 x 10^{27} atoms is m = 2.96 x 10^{3} kg$

Hence the mass of uranium is 2.96x10³kg

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Most popular questions from this chapter

Could a $56 Fe$ nucleus fission into two $28 Al$ nuclei? Your answer, which should include some calculations, should be based on the curve of binding energy.

The barium isotope ¹³¹Ba has a half-life of 12 days. A 250 $μ$ mg

sample of ¹³¹Ba is prepared. What is the mass of ¹³¹Ba after

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The half-life of the uranium isotope ${}^{235}U$ is $700$ million years. The earth is approximately localid="1650486537957" $4.5$ billion years old. How much more ${}^{235}U$ was there when the earth formed than there is today? Give your answer as the then-to-now ratio.

Use the potential-energy diagram in Figure $42.8$ to estimate the ratio of the gravitational potential energy to the nuclear potential energy for two neutrons separated by $1.0$ $f m$ .

What energy (in MeV) alpha particle has a de Broglie wavelength equal to the diameter of a 238 U nucleus?

See all solutions

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