Home
Class 12
PHYSICS
A source contains two phosphorus radionu...

A source contains two phosphorus radionuclei `._15^32P (T_(1//2) =14.3 d)` and `._15^33P (T_(1//2) = 25.3 d)`. Initially, 10% of the decay come from `._15^33P`. How long one must wait until 90% comes from it?

Text Solution

Verified by Experts

Let `R_(01)` and `R_(02)` be the initial activities of `._15^33P` and `._15^32P` respectively and `R_1` and `R_2` be their activities at any instant t. According to the first observation ,
`R_(01) =10% (R_(01) +R_(02))`
or , `R_(02) = 9R_(01)`.....(1)
Again, `R_1=90% (R_1+R_2)`
or, `R_2=R_1/9`...(2)
Combining equation (1) and (2),
`R_2/R_(02) =1/81 R_1/R_(01)`
or, `(R_(02)e^(-lambda_2t))/R_(02) =1/81xx(R_(01)e^(-lambda_1t))/R_(01)`
or, `81e^(-lambda_2t) = e^(-lambda_1t)`
or, `(lambda_2-lambda_1) t ` = 2.303 log 81
`therefore t=(2.303 log81)/(0.693/14.3-0.693/25.3) [ because lambda=0.693/T_(1//2)]`
=208.5 d
Promotional Banner

Topper's Solved these Questions

  • ATOMIC NUCLEUS

    CHHAYA PUBLICATION|Exercise NCERT EXEMPLAR QUESTION|6 Videos

  • ATOMIC NUCLEUS

    CHHAYA PUBLICATION|Exercise EXERCISE|85 Videos

  • ATOMIC NUCLEUS

    CHHAYA PUBLICATION|Exercise HOTS QUESTION|14 Videos

  • ATOM

    CHHAYA PUBLICATION|Exercise CBSE SCANNER|18 Videos

  • CAPACITANCE AND CAPACITOR

    CHHAYA PUBLICATION|Exercise CBSE SCANNER|15 Videos

Similar Questions

Explore conceptually related problems

A computer producing factory has only two plants T_(1) "and" T_(2) "Plant" T_(1) produces 20% and plant T_(2) produced 80% of the total computers produced. 7% of computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective, given that it is produced in plant T_(1) = 10 P (computer turns out to be defective, given that it is produced in plant T_(2) )where P(E) denptes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T_(2) is

A computer producing factory has only two plants T_(1) and T_(2). Plant T_(1) produces 20% and plant T_(2) produces 80% of the total computers produced in the factory turn out to be defective. It is known that P (computer turns out to be defective givent that it is produced in plant T_(1)) = 10 P ( computer turns out to be defective given that it is produced in plant T_(2)), where P (E) denotes the probability of an event E. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T_(2) is

How many molecules of CO_2 are present in one litre of air containing 0.03% volume of CO_2 at N.T.P.?

Let {t_n} be a sequence of integers in G.P. in which t_4: t_6=1:4 and t_2+t_5=216. Then t_1 is (a). 12 (b). 14 (c). 16 (d). none of these

Calculate the rate constant and time required to complete 90% reaction for a first order reaction having t_(1/2) = 30 minutes. Find t_(1/2) for a 2nd order reaction K = 4.3xx10^-4 mol^-1 lit sec^-1 and initial conc. 0.24 (M).

In R^(3) , consider the planes P_(1):y=0 and P_(2),x+z=1. Let P_(3) be a plane, different from P_(1) and P_(2) which passes through the intersection of P_(1) and P_(2) , If the distance of the point (0,1,0) from P_(3) is 1 and the distance of a point (alpha,beta,gamma) from P_(3) is 2, then which of the following relation(s) is/are true? (a) 2alpha + beta + 2gamma +2 = 0 (b) 2alpha -beta + 2gamma +4=0 (c) 2alpha + beta - 2gamma- 10 =0 (d) 2alpha- beta+ 2gamma-8=0

The sum of values of x satisfying the equation (31+8sqrt(15))^(x^2-3)+1=(32+8sqrt(15))^(x^2-3) is (a) 3 (b) 0 (c) 2 (d) none of these

A magnetic dipole is under the influence fof two magnetic fields .The influence of two magnetic fields . The angle between the field directions us 60^(@) and one of the fields has a magnitude of 1.2xx10^(-2)T . If the the dipole comes to stable equilibrium at an angle of 15^(@) with this field , what is the magnitude of the other field ?

Football teams T_(1)and T_(2) have to play two games are independent. The probabilities of T_(1) winning, drawing and lossing a game against T_(2) are 1/6,1/6and 1/3, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_(1) and T_(2) respectively, after two games. P(X=Y) is

A bag contains 20 coins. If the probability that the bag contains exactly 4 biased coin is 1/3 and that of exactly 5 biased coin is 2/3 , then the probability that all the biased coin are sorted out from bag is exactly 10 draws is a. 5/(10)(.^(16)C_6)/(.^(20)C_9)+1/(11)(.^(15)C_5)/(.^(20)C_9) b. 2/(33)[(.^(16)C_6+5 .^(15)C_5)/(.^(20)C_9)] c. 5/(33)(.^(16)C_7)/(.^(20)C_9)+1/(11)(.^(15)C_6)/(.^(20)C_9) d. none of these