Problem 5.65 Part A Calcium-47, which decays by beta emission, has a half-life o
ID: 546830 • Letter: P
Question
Problem 5.65 Part A Calcium-47, which decays by beta emission, has a half-life of 4.5 days Write the nuclear equation for the beta decay of calcium-47, Express your answer as a nuclear equation. Submit My Answers Give Up Incorrect; Try Again; 4 attempts remaining; no points deducted Part B How many milligrams of an initial 46 mg of calcium-47 remain after 18 days ? Express your answer using two significant figures. mg Submit My Answers Give Up Part C How many days are required for 19.2 mg of calcium-47 to decay to 1.2 mg? Express your answer using two significant figures.Explanation / Answer
Part A : The beta decay of Ca-47 is as follows:
20Ca47 ---> 21Sc47 + -1e0
Part B :
We know that all radio active nuclei undergoes first order reaction.
For a first order reaction rate constant , k = ( 2.303 /t )x log ( Mo / M)
Where
k = rate constant = 0.693 / half life
= 0.693 /4.5 days
= 0.154 day-1
Mo = initial mass = 46 mg
M= Mass left after time t = ?
t = time = 18 days
Plug the values we get
log ( Mo / M) = ( kt)/2.303
= 1.204
Mo / M = 101.204 = 16.0
M = 46 mg / 16.0 = 2.9 mg
Part C :
For a first order reaction rate constant , k = ( 2.303 /t )x log ( Mo / M)
Where
k = rate constant = 0.693 / half life
= 0.693 /4.5 days
= 0.154 day-1
Mo = initial mass = 19.2 mg
M= Mass left after time t = 1.2 mg
t = time = ?
Plug the values we get t = ( 2.303 /k)x log ( Mo / M)
= 18.0 days