Chapter 42: Q 19 Exercise (page 1236)

The radium isotope ²²⁶Ra has a half-life of 1600 years. A
sample begins with 1.00x10¹⁰ ²²⁶Ra atoms. How many are left
after (a) 200 years, (b) 2000 years, and (c) 20,000 years?

Short Answer

Expert verified

Therefore,

$a.) N = 9.17 \times 10^{9} atoms b.) N = 4.20 \times 10^{9} atoms c.) N = 1.73 \times 10^{6} atoms$

Step by step solution

Given information

$t_{1 / 2} = 1600 years N_{o} = 1.0 \times 10^{10} atoms$

Explanation (a)

(a)After t = 200 years, we must determine the number of nuclei ²²⁶Ra that remain.

$N = N_{o} {(\frac{1}{2})}^{t / t_{1 / 2}} N = (1.0 \times 10^{10} atoms) {(\frac{1}{2})}^{200 years / 1600 years} N = (1.0 \times 10^{10} atoms) {(\frac{1}{2})}^{0.125} N = (1.0 \times 10^{10} atoms) \times (0.9170) N = 9.17 \times 10^{9} atoms$

Explanation (b)

(b)After t = 2000 years, we must determine the number of nuclei ²²⁶Ra that remain.

$N = N_{o} {(\frac{1}{2})}^{t / t_{1 / 2}} N = (1.0 \times 10^{10} atoms) {(\frac{1}{2})}^{2000 years / 1600 years} N = (1.0 \times 10^{10} atoms) {(\frac{1}{2})}^{125} N = (1.0 \times 10^{10} atoms) \times (0.42044) N = 4.20 \times 10^{9} atoms$

Explanation (c)

(c)After t = 20000 years, we must determine the number of nuclei ²²⁶Ra that remain.

$N = N_{o} {(\frac{1}{2})}^{t / t_{1 / 2}} N = (1.0 \times 10^{10} atoms) {(\frac{1}{2})}^{20000 years / 1600 years} N = (1.0 \times 10^{10} atoms) {(\frac{1}{2})}^{12.5} N = (1.0 \times 10^{10} atoms) \times (0.00017) N = 1.73 \times 10^{6} atoms$

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The radium isotope ²²⁶Ra has a half-life of 1600 years. A
sample begins with 1.00x10¹⁰ ²²⁶Ra atoms. How many are left
after (a) 200 years, (b) 2000 years, and (c) 20,000 years?

Short Answer

Step by step solution

Given information

Explanation (a)

Explanation (b)

Explanation (c)

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The radium isotope 226Ra has a half-life of 1600 years. Asample begins with 1.00x1010 226Ra atoms. How many are leftafter (a) 200 years, (b) 2000 years, and (c) 20,000 years?

Short Answer

Step by step solution

Given information

Explanation (a)

Explanation (b)

Explanation (c)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Physical Quantities And Units

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Study anywhere. Anytime. Across all devices.

The radium isotope ²²⁶Ra has a half-life of 1600 years. A
sample begins with 1.00x10¹⁰ ²²⁶Ra atoms. How many are left
after (a) 200 years, (b) 2000 years, and (c) 20,000 years?