Q 19 Exercise The radium isotope 226Ra has a h... [FREE SOLUTION]

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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,

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

Step by step solution

Given information

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

Explanation (a)

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

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

Explanation (b)

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

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

Explanation (c)

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

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

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91影视

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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91影视

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

Linear Momentum

Oscillations

Dynamics

Space Physics

Electrostatics

Engineering Physics

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?