In: Chemistry

# the half-life of a radioisotope 63 hours how much time will elapse if the radioisotope decays...

the half-life of a radioisotope 63 hours how much time will elapse if the radioisotope decays to one-fourth of its original mass?

## Solutions

##### Expert Solution

Ans:

Let the original mass be m1

Let the molar mass of the isotope be ‘M’.

No. of isotope initially, No = (m1/M) x NA                               {NA = Avagadro’s no = 6.023 x 1023}

Mass after the decay, m2 = m1/4

No. of isotopes after the decay, Nt = (m2/M) x NA = (m1/4M) x NA

Half-life, t½ = 63 hours

λ = decay constant = 0.693/t½ = 0.693/63 = 0.011 hours-1

We know that all radioactive decay follows first order kinetics. Accordingly, we have

Nt = No . e(-λt)

where, Nt = no of radioactive isotopes after the decay

No = Initial no of radioactive isotopes

λ = decay constant

t = time taken for decay =?

(m1/4M) x NA = {(m1/M) x NA} e(-0.011 x t)

t = 126 hours

OR

In a first order reaction for original mass to become half, it takes 1 half-life. For original mass to become 1/4th of its original mass it takes 2 half-life.

So, t = 2t½ = 2 x 63 = 126 hours

## Related Solutions

##### If 13% of Americium decays in 7 hours, what is the half-life of Americium in hours?...
If 13% of Americium decays in 7 hours, what is the half-life of Americium in hours? Round your answer to 3 decimal places.
##### The half-life of 99mTc is 6 hours. After how much time will 1/16th of the radioisotope...
The half-life of 99mTc is 6 hours. After how much time will 1/16th of the radioisotope remain?
##### A drug with a half-life of 15 hours is administered by continuous intravenous infusion. How long...
A drug with a half-life of 15 hours is administered by continuous intravenous infusion. How long will it take for the drug to reach 75% of its final steady-state level?
##### 81Sr decays by positron emission with a half-life of 22.2 minutes. Starting with 885g of Sr-81,...
81Sr decays by positron emission with a half-life of 22.2 minutes. Starting with 885g of Sr-81, how much remains after 75.0 minutes?
##### The​ half-life of radium is 1690 years. If 60 grams are present​ now, how much will...
The​ half-life of radium is 1690 years. If 60 grams are present​ now, how much will be present in 460 ​years?
##### An employee receives an hourly rate of $15, with time and a half for all hours... An employee receives an hourly rate of$15, with time and a half for all hours worked in excess of 40 during the week. Payroll data for the first week of the calendar year are as follows: hours worked, 46; federal income tax withheld, $110, Social security tax rate,6%; and Medicare tax rate, 1.5%; state unemployment tax, 5.4% on the fast$7,000; federal unemployment tax, 0.81% on the first $7,000. What is the net amount to be paid to the... ##### Sadie White receives an hourly rate of$30, with time and a half for all hours...
Sadie White receives an hourly rate of $30, with time and a half for all hours worked in excess of 40 during a week. Payroll data for the current week are as follows: hours worked, 48; federal income tax withheld,$300; social security tax rate, 6.0%; and Medicare tax rate, 1.5%. What is the net amount to be paid to White? $1,143.00$1,260.00 $1,443.00$1,000.00
##### Phosphorus-32 decays by beta emission to form sulfur-32. How many half-lives have passed in the...
Part APhosphorus-32 decays by beta emission to form sulfur-32. How many half-lives have passed in the reaction shown here?Part BThe half-life of phosphorus-32 is 14.26 days. Calculate its decay constant.Radioactive decay is characterized by the equation where No is the initial amount, N is the amount remaining at time, and k is the rate constant. The half-life ()is the time required for the number of radioactive nuclei in a sample to drop to half of its initial value. It is...
##### How much customers buy is a direct result of how much time they spend in the...
How much customers buy is a direct result of how much time they spend in the store. A study of average shopping times in a large national houseware store gave the following information (Source: Why We Buy: The Science of Shopping by P. Underhill). Women with female companion: 8.3 min. Women with male companion: 4.5 min. Suppose you want to set up a statistical test to challenge the claim that a woman with a female friend spends an average of...