Advertisements
Advertisements
Question
The half-life of 35S is 87.8 d. What percentage of 35S sample remains after 180 d?
Advertisements
Solution
Given: t1/2 = 87.8 d, N0 = 100, t = 180 d
To find: % of 35S that remains after 180 days
Formulae:
- `lambda = 0.693/("t"_(1//2))`
- `lambda = 2.303/"t" log_10 ("N"_0/"N")`
Calculation:
- `lambda = 0.693/("t"_(1//2)) = 0.693/(87.8 "d") = 7.893 xx 10^-3 "d"^-1`
- Now, `lambda = 2.303/"t" log_10 ("N"_0/"N")`
`log_10 ("N"_0/"N") = (lambda"t")/2.303`
`= (7.893 xx 10^-3 xx 180)/2.303`
= 0.617
Taking antilog on both sides we get,
`"N"_0/"N" = 4.140`
N = `100/4.140`
= 24.155 ≈ 24.2%
Percentage of 35S that remains after 180 d is 24.2%.
APPEARS IN
RELATED QUESTIONS
What is gamma decay?
Complete the following equation describing nuclear decay.
\[\ce{_90^228Th->\alpha { +}}\] _____
Choose the correct option.
\[\ce{^60_27CO}\] decays with a half-life of 5.27 years to produce \[\ce{^60_28Ni}\]. What is the decay constant for such radioactive disintegration?
Write relation between decay constant of a radioelement and its half-life.
The half-life of 18F is 110 minutes. What fraction of 18F sample decays in 20 minutes?
A 3/4 of the original amount of radioisotope decays in 60 minutes. What is its half-life?
A sample of 32P initially shows activity of one Curie. After 303 days, the activity falls to 1.5 × 104 dps. What is the half-life of 32P?
The decay constant λ of a certain radioactive material is 0.2166 per day. The average life τ of the radioactive material is ______
The half-life of a certain radioactive species is 6.93 × 105 seconds. What is the decay constant?
Show that half life period of radioactive material varies inversely to decay constant λ.
Show that for radioactive decay N(t) = `"N"_"O" "e"^{-λ"t"}`, where symbols have their usual meaning.
Obtain an expression for the half-lifetime of radioactive material. Hence state the relation between an average life and half life time of radioactive material.
A radioactive substance decays to (1/10)th of its original value in 56 days. Calculate its decay constant.
A radioactive nucleus emits 4 α-particles and 7 β-particles in succession. The ratio of number of neutrons of that of protons, is
[A = mass number, Z =atomic number]
A radioactive substance of half-life 69.3 days is kept in a container. The time in which 80% of the substance will disintegrate will be ______
[take ln(5) = 1.61]
Most excited states of an atom have life times of about ____________.
A radioactive substance has half life of 3 hours. 75 % of the substance would decay in ____________.
What is alpha decay?
What is beta decay?
The activity of a radioactive substance decreases by a factor of 32 in one hour. The half-life of the substance (in min) is ______.
A radioactive sample S1 having the activity A1 has twice the number of nuclei as another sample S2 of activity A2 If A2 = 2A1 then the ratio of half-life of S1 to the half-life of S2 is ______.
The half-life of a radioactive substance is 10 days. The time taken for the `(7/8)^"th"` of the sample of disintegrates is ______.
The disintegration rate of a radio-active sample is 1010 per hour at 20 hours from the start. It reduces to 5 × 109 per hour after 30 hours. Calculate the decay constant.
If the number of nuclei of a radioactive substance becomes `1/e` times the initial number in 10 days, what is the decay constant of the substance?
