###### Advertisements

###### Advertisements

What is the amount of \[\ce{_27^60Co}\] necessary to provide a radioactive source of strength 10.0 mCi, its half-life being 5.3 years?

###### Advertisements

#### Solution

**Data:** Activity= 10.0 mCi = 10.0 x 10^{-3} Ci = (10.0 x 10^{-3})(3.7 x 10^{10}) dis/s = 3.7 x 10^{8} dis/s

T_{1/2} = 5.3 years = (5.3)(3.156 × 10^{7})s = 1.673 × 10^{8} s

Decay constant, `lambda = 0.693/("T"_(1//2)) = 0.693/(1.673 xx 10^8) "s"^-1`

= 4.142 x 10^{-9} s^{-1}

∴ N = `"activity"/lambda = (3.7 xx 10^8)/(4.142 xx 10^-9)` atoms

= 8.933 × 10^{16} atoms

= 60 grams of \[\ce{_27^60Co}\] contain 6.02 x 10^{23} atoms

∴ Mass of 8.933 x 10^{16} atoms of \[\ce{_27^60Co}\]

`= (8.933 xx 10^16)/(6.02 xx 10^23) xx 60 "g"`

= 8.903 x 10^{-6} g = 8.903 µg

#### APPEARS IN

#### RELATED QUESTIONS

The decay constant of radioactive substance is 4.33 x 10^{-4} per year. Calculate its half life period.

State the law of radioactive decay.

Derive the mathematical expression for law of radioactive decay for a sample of a radioactive nucleus

Obtain the relation between the decay constant and half life of a radioactive sample.

Why is it found experimentally difficult to detect neutrinos in nuclear β-decay?

The Q value of a nuclear reaction \[\ce{A + b → C + d}\] is defined by

Q = [ m_{A}+ m_{b}− m_{C}− m_{d}]c^{2 }where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic.

\[\ce{^1_1H + ^3_1H -> ^2_1H + ^2_1H}\]

Atomic masses are given to be

`"m"(""_1^2"H")` = 2.014102 u

`"m"(""_1^3"H")` = 3.016049 u

`"m"(""_6^12"C")` = 12.000000 u

`"m"(""_10^20"Ne")` = 19.992439 u

Represent Radioactive Decay curve using relation `N = N_o e^(-lambdat)` graphically

A radioactive nucleus 'A' undergoes a series of decays as given below:

The mass number and atomic number of A_{2} are 176 and 71 respectively. Determine the mass and atomic numbers of A_{4} and A.

Using the equation `N = N_0e^(-lambdat)` obtain the relation between half-life (T) and decay constant (`lambda`) of a radioactive substance.

(a) Derive the relation between the decay constant and half life of a radioactive substance.

(b) A radioactive element reduces to 25% of its initial mass in 1000 years. Find its half life.

Two different radioactive elements with half lives T_{1} and T_{2} have N_{1} and N_{2} undecayed atoms respectively present at a given instant. Derive an expression for the ratio of their activities at this instant in terms of N_{1} and N_{2 ?}

The radioactive isotope D decays according to the sequence

If the mass number and atomic number of D_{2} are 176 and 71 respectively, what is (i) the mass number (ii) atomic number of D?

In a radioactive decay, neither the atomic number nor the mass number changes. Which of the following particles is emitted in the decay?

Lithium (*Z* = 3) has two stable isotopes ^{6}Li and ^{7}Li. When neutrons are bombarded on lithium sample, electrons and α-particles are ejected. Write down the nuclear process taking place.

The masses of ^{11}C and ^{11}B are respectively 11.0114 u and 11.0093 u. Find the maximum energy a positron can have in the β*-decay of ^{11}C to ^{11}B.

(Use Mass of proton m_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

Calculate the maximum kinetic energy of the beta particle emitted in the following decay scheme:^{12}N → ^{12}C* + *e*^{+} + *v*^{12}C* → ^{12}C + γ (4.43MeV).

The atomic mass of ^{12}N is 12.018613 u.

(Use Mass of proton m_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

The decay constant of ^{238}U is 4.9 × 10^{−18} S^{−1}. (a) What is the average-life of ^{238}U? (b) What is the half-life of ^{238}U? (c) By what factor does the activity of a ^{238}U sample decrease in 9 × 10^{9} years?

^{57}Co decays to ^{57}Fe by β^{+}- emission. The resulting ^{57}Fe is in its excited state and comes to the ground state by emitting γ-rays. The half-life of β^{+}- decay is 270 days and that of the γ-emissions is 10^{−8} s. A sample of ^{57}Co gives 5.0 × 10^{9} gamma rays per second. How much time will elapse before the emission rate of gamma rays drops to 2.5 × 10^{9}per second?

When charcoal is prepared from a living tree, it shows a disintegration rate of 15.3 disintegrations of ^{14}C per gram per minute. A sample from an ancient piece of charcoal shows ^{14}C activity to be 12.3 disintegrations per gram per minute. How old is this sample? Half-life of ^{14}C is 5730 y.

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t_{1}_{/2}. Show that after a time t >> t_{1}_{/2} the number of active nuclei will become constant. Find the value of this constant.

The half-life of ^{40}K is 1.30 × 10^{9} y. A sample of 1.00 g of pure KCI gives 160 counts s^{−1}. Calculate the relative abundance of ^{40}K (fraction of ^{40}K present) in natural potassium.

Obtain a relation between the half-life of a radioactive substance and decay constant (λ).

Disintegration rate of a sample is 10^{10} per hour at 20 hours from the start. It reduces to 6.3 x 10^{9} per hour after 30 hours. Calculate its half-life and the initial number of radioactive atoms in the sample.

The isotope \[\ce{^57Co}\] decays by electron capture to \[\ce{^57Fe}\] with a half-life of 272 d. The \[\ce{^57Fe}\] nucleus is produced in an excited state, and it almost instantaneously emits gamma rays.

(a) Find the mean lifetime and decay constant for ^{57}Co.

(b) If the activity of a radiation source ^{57}Co is 2.0 µCi now, how many ^{57}Co nuclei does the source contain?

c) What will be the activity after one year?

A source contains two species of phosphorous nuclei, \[\ce{_15^32P}\] (T_{1/2} = 14.3 d) and \[\ce{_15^33P}\] (T_{1/2} = 25.3 d). At time t = 0, 90% of the decays are from \[\ce{_15^32P}\]. How much time has to elapse for only 15% of the decays to be from \[\ce{_15^32P}\]?

Before the year 1900 the activity per unit mass of atmospheric carbon due to the presence of ^{14}C averaged about 0.255 Bq per gram of carbon.

(a) What fraction of carbon atoms were ^{14}C?

(b) An archaeological specimen containing 500 mg of carbon, shows 174 decays in one hour. What is the age of the specimen, assuming that its activity per unit mass of carbon when the specimen died was equal to the average value of the air? The half-life of ^{14}C is 5730 years.

Obtain an expression for the decay law of radioactivity. Hence show that the activity A(t) =λN_{O} e^{-λt}.

Two radioactive materials X_{1} and X_{2} have decay constants 10λ and λ respectively. If initially, they have the same number of nuclei, then the ratio of the number of nuclei of X_{1} to that of X_{2} will belie after a time.

A radioactive element disintegrates for an interval of time equal to its mean lifetime. The fraction that has disintegrated is ______

Which one of the following nuclei has shorter meant life?

'Half-life' of a radioactive substance accounts for ______.

The half-life of a radioactive sample undergoing `alpha` - decay is 1.4 x 10^{17} s. If the number of nuclei in the sample is 2.0 x 10^{21}, the activity of the sample is nearly ____________.

After 1 hour, `(1/8)^"th"` of the initial mass of a certain radioactive isotope remains undecayed. The half-life of the isotopes is ______.

Two radioactive materials Y_{1} and Y_{2} have decay constants '5`lambda`' and `lambda` respectively. Initially they have same number of nuclei. After time 't', the ratio of number of nuclei of Y_{1} to that of Y_{2 }is `1/"e"`, then 't' is equal to ______.

What percentage of radioactive substance is left after five half-lives?

Two electrons are ejected in opposite directions from radioactive atoms in a sample of radioactive material. Let c denote the speed of light. Each electron has a speed of 0.67 c as measured by an observer in the laboratory. Their relative velocity is given by ______.

The half-life of a radioactive nuclide is 20 hrs. The fraction of the original activity that will remain after 40 hrs is ______.

If 10% of a radioactive material decay in 5 days, then the amount of original material left after 20 days is approximately :

The half-life of the radioactive substance is 40 days. The substance will disintegrate completely in

Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half life of 1 year. After 1 year ______.

Samples of two radioactive nuclides A and B are taken. λ_{A} and λ_{B} are the disintegration constants of A and B respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time?

- Initial rate of decay of A is twice the initial rate of decay of B and λ
_{A}= λ_{B}. - Initial rate of decay of A is twice the initial rate of decay of B and λ
_{A}> λ_{B}. - Initial rate of decay of B is twice the initial rate of decay of A and λ
_{A}> λ_{B}. - Initial rate of decay of B is the same as the rate of decay of A at t = 2h and λ
_{B}< λ_{A}.

Which sample, A or B shown in figure has shorter mean-life?

The radioactivity of an old sample of whisky due to tritium (half-life 12.5 years) was found to be only about 4% of that measured in a recently purchased bottle marked 10 years old. The age of a sample is ______ years.

What is the half-life period of a radioactive material if its activity drops to 1/16^{th} of its initial value of 30 years?

The half-life of `""_82^210Pb` is 22.3 y. How long will it take for its activity 0 30% of the initial activity?