Home
Class 12
PHYSICS
Uranium "(92)^(238)U is an unstable nuc...

Uranium `"_(92)^(238)U` is an unstable nucleaus. It decays to Thorium `"_(90)^(234)Th`, which is again an unstable nuclei which further decays to `"_(91)^(234)Pa`. Such decay is called successive dlsntegration. Let `"_(92)^(238)U` is called as `A` of decay constant `lambda_(1)` and `"_(90)^(234)Th` is called as `B` of decay constant `lambda_(2)` and stable nuclei `"_(91)^(234)Pa` is named as `C`. Here `A` is called parent nucleus and `B` is called daughter nucleus of `A`. Any two adjacent nuclei may be consider parem daughter nuclei. Suppose `N_(1)`, `N_(2)` and `N_(3)` are number of nuclei `A`, `B` and `C` respectively at time `t` which undergoes decay. Then we can write
`Aoverset(lambda_(2))(to)Boverset(lambda_(2))(to)C`
Rate of disintegration of `A=(dN_(1))/(dt)= -lambda_(1)N_(1)`
Rate of disintegration of `B= -lambda_(2)N_(2)` and net rate of formation of `B=(dN_(2))/(dt)=lambda_(1)N_(1)-lambda_(2)N_(2)`
Rate of formation of nuclei `C` is equal to `(dN_(3))/(dt)=lambda_(2)N_(2)`
If at `t=0`, there are `N_(0)` number of nuclei of `A`, where as nuclei `B` and `C` are absent in the sample answer the following questions
Number of nuclei of `B` at any time `t` is

A

`N_0[1+(lambda_1)/(lambda_2 -lambda_1)e^(-lamda_2t)-(lambda_2)/(lambda_2-lambda_1)e^(-lambda_1t)]`

B

`N_0[(lambda_1)/(lambda_2 -lambda_1)e^(-lamda_2t)-(lambda_2)/(lambda_2-lambda_1)e^(-lambda_1t)]`

C

`N_0(lambda_1)/(lambda_2 -lambda_1)(e^(-lamda_2t)-e^(-lambda_1t))`

D

`N_0[(lambda_1)/(lambda_2-lambda_1)e^(-lambda_2t)-(lambda_2)/(lambda_2-lambda_1)e^(-lambda_1t)-1]`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Similar Questions

Explore conceptually related problems

Uranium "_(92)^(238)U is an unstable nucleaus. It decays to Thorium "_(90)^(234)Th , which is again an unstable nuclei which further decays to "_(91)^(234)Pa . Such decay is called successive dlsntegration. Let "_(92)^(238)U is called as A of decay constant lambda_(1) and "_(90)^(234)Th is called as B of decay constant lambda_(2) and stable nuclei "_(91)^(234)Pa is named as C . Here A is called parent nucleus and B is called daughter nucleus of A . Any two adjacent nuclei may be consider parem daughter nuclei. Suppose N_(1) , N_(2) and N_(3) are number of nuclei A , B and C respectively at time t which undergoes decay. Then we can write Aoverset(lambda_(2))(to)Boverset(lambda_(2))(to)C Rate of disintegration of A=(dN_(1))/(dt)= -lambda_(1)N_(1) Rate of disintegration of B= -lambda_(2)N_(2) and net rate of formation of B=(dN_(2))/(dt)=lambda_(1)N_(1)-lambda_(2)N_(2) Rate of formation of nuclei C is equal to (dN_(3))/(dt)=lambda_(2)N_(2) If at t=0 , there are N_(0) number of nuclei of A , where as nuclei B and C are absent in the sample answer the following questions The graph between N_(1) , N_(2) & N_(3) with time can be best represented by

Uranium ._(92)^(238)U is an ustable nucleus. It decays to Thorium ._(92)^(238)Th , which is again an unstable nucleus which further decays to ._(91)^(234)Pa . Let ._(92)^(238)U be called A of decay constant lambda_(1) and ._(90)^(234)Th is called as B of decay constant lambda_(2) and stable nuclei ._(91)^(234)Pa be called as C . Here A is called parent nucleus and B is called daughter nucleus of A . Any two adjacent nuclei may be consider parent or daughter nuclei A, B and C respectively at time 't' . Then we can write Aoverset(lambda_(1))rarrBoverset(lambda_(2))rarrC Rate of disintergration of A=(dN_(1))/(dt)=-lambda_(1)N_(1) Rate of disintergration of B=(dN_(2))/(dt)=lambda_(1)N_(1)-lambda_(2)N_(2) Rate of formation of nuclei C is equal to (dN_(3))/(dt)=-lambda_(2)N_(2) If at t=0 , there are N_(0) number of nuclei of A where as nuclei B and C are absent in the sample Answer the following questions ltbgt Numeber of the nuclei of nuclei C at time t is

Uranium ._(92)^(238)U is an ustable nucleus. It decays to Thorium ._(92)^(238)Th , which is again an unstable nucleus which further decays to ._(91)^(234)Pa . Let ._(92)^(238)U be called A of decay constant lambda_(1) and ._(90)^(234)Th is called as B of decay constant lambda_(2) and stable nuclei ._(91)^(234)Pa be called as C . Here A is called parent nucleus and B is called daughter nucleus of A . Any two adjacent nuclei may be consider parent or daughter nuclei A, B and C respectively at time 't' . Then we can write Aoverset(lambda_(1))rarrBoverset(lambda_(2))rarrC Rate of disintergration of A=(dN_(1))/(dt)=lambda_(1)N_(1) Rate of disintergration of B=(dN_(2))/(dt)=lambda_(1)N_(1)-lambda_(2)N_(2) Rate of formation of nuclei C is equal to (dN_(3))/(dt)=lambda_(2)N_(2) If at t=0 , there are N_(0) number of nuclei of A where as nuclei B and C are absent in the sample Answer the following questions Number of nuclei of B at any time t is

At time t=0 N_(1) nuclei of decay constant lambda_(1)& N_(2) nuclei of decay constant lambda_(2) are mixed. The decay rate of the mixture at time 't' is:

._(92)^(238)U has 92 protons and 238 nucleons. It decays by emitting an alpha particle and becomes:

The decay constant (lambda) for radioactive decay is independent of

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then :

Nucleus A decays to B with decay constant lambda_(1) and B decays to C with decay constant lambda_(2) . Initially at t=0 number of nuclei of A and B are 2N_(0) and N_(0) respectively. At t=t_(o) , no. of nuclei of B is (3N_(0))/(2) and nuclei of B stop changing. Find t_(0) ?

A radioactive nucleus ._92 X^235 decays to ._91 Y^231 . Which of following particles are emitted ?

A parent radioactive nucleus A (decay constant lamda_(A)) converts into a radio-active nucleus B of decay constant lamda_(b) , initially, number of atoms of B is zero At any time N_(a),N_(b) are number of atoms of nuclei A and B respectively then maximum velue of N_(b) .