To find: The amount remaining bismuth-210 after 15 days.
The amount remaining bismuth-210 after 15 days is 25mg.
The half-life of bismuth-210 is 5 days.
The mass of sample bismuth-210 = 200 mg.
Let be the initial mass of bismuth-210.
That is .
After 5 days the bismuth level is
Substitute 200mg for in ,
After 10 days the bismuth level is
Substitute 100mg for in ,
After 15 days the bismuth level is
Substitute 50mg for in ,
Therefore, the amount of bismuth after 15 days is 25mg.
To find: The amount of bismuth after t days.
After t days mass of bismuth is .
Consider half –life bismuth mass in 5 days =
After .where x be variable.
Therefore after t days mass of bismuth as follows,
Substitute for x and 200 for in equation (1),
Therefore, after t days mass of bismuth is .
To estimate: The remaining amount of bismuth after 3 weeks.
After 3 weeks the amount of bismuth is .
Consider after 5 days the amount of bismuth = 100 mg.
After 5 days the amount of bismuth is
By using part (b) solution for t days.
Obtain the amount after 3 weeks that means 21 days.
Substitute 21 for t in ,
Therefore, after 3 weeks the amount of bismuth is .
To estimate: The amount of bismuth reduced to 1mg.
The amount of bismuth mass reduced to 1mg for 38.2215 days.
The reduced amount of bismuth = 1mg.
Let x axis for days and y axis for bismuth (mg).
Using online graphing calculator to draw the graphs for bismuth level and days as shown below Figure 1.
Observe the graph, an initial stage bismuth mass is 200 mg.
Then after 5 days the mass is reducing to 100 mg.
After 10 the mass is reducing to 50 mg.
After 15 days mass is reducing to 25 mg.
Therefore, the mass of bismuth is reducing when the days are increasing.
From the graph, the general form of bismuth after t days .
Substitute 1 for in ,
Take naturel logarithm on both sides,
Therefore, the amount of bismuth mass reduced to 1mg for 38.2215 days.
Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!