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4th Edition

James Stewart

Publisher: Cengage Learning

ISBN: 9781337687805

Chapter 1.5, Problem 32E

(a)

To determine

**To find:** The amount remaining isotope of sodium after 60 hours.

Expert Solution

The amount remaining isotope of sodium after 60 hours is 0.125g.

**Given:**

The half-life of sodium is 15 hours.

The mass of sample sodium = 2g.

**Calculation:**

Let

That is

After 15 hours the amount of sodium is

Substitute 2g for

After 30 hours the amount of sodium

Substitute 1g for

After 45 hours the amount of sodium is

Substitute 0.5g for

After 60 hours the amount of sodium is

Substitute 0.25g for

Therefore, the amount sodium after 60 hours is 0.125g.

(b)

To determine

**To find:** The amount of sodium after *t* hours.

Expert Solution

After *t* hours amount of sodium is

**Calculation:**

Consider half –life sodium amount in 15 hours =

Where

After
*x* be variable.

Therefore after *t* hours amount of sodium as follows,

Substitute
*x* and 2 for

Therefore, after *t* hours amount of sodium is

(c)

To determine

**To estimate:** The remaining amount of sodium after 4 days.

Expert Solution

After 4days the amount of sodium is

**Given:**

Consider after 15 hours the amount of sodium = 1g.

**Calculation:**

After 15 hours the amount of sodium is

By using part (b) solution
*t* hours.

Obtain the amount after 4 days that means 96 hours.

Substitute 96 for *t* in

Therefore, after 4 days the amount of sodium is

(d)

To determine

**To estimate:** The amount of bismuth reduced to 0.01g.

Expert Solution

The amount of sodium amount reduced to 0.01g for 38.2215 days.

**Given:**

The reduced amount of sodium = 0.01g.

**Graph:**

Let *x* axis for hours and *y* axis for sodium (g).

Use the online graphing calculator and draw the graphs for sodium level and hours as shown below Figure 1.

Observe the graph an initial stage sodium amount is 2g.

Then after 15 hours the mass is reducing to 1g.

After 30 hours the mass is reducing to 0.5g.

After 45 hours mass is reducing to 0.25g.

After 60 hours mass is reducing to 0.125g.

Therefore, the mass of sodium is reducing when the hours are increasing.

**Calculation:**

From the graph, the general form of sodium after *t* hours

Substitute 0.01 for

Take naturel logarithm on both sides,

Simplify further,

Therefore, the amount of sodium reduced to 0.01g for 114.6645 hours.