+91-8076753736[email protected]
logo
logo
-->

Wave Optics

Question
CBSEENPH12039886
Wired Faculty App

A radio isotope X with a half life 1.4 x 109 yr decays of Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1:7. The age of the rock is,

  • 1.96 x 109 yr

  • 3.92 x 109 yr

  • 4.20 x 109 yr

  • 8.40 x 109 yr

Solution

C.

4.20 x 109 yr

Ratio of X:Y is given = 1:7
That is,
straight m subscript straight x over straight m subscript straight y equals 1 over 7
rightwards double arrow space 7 straight m subscript straight x space equals space straight m subscript straight y
Let, the initial total mass is m.

rightwards double arrow space straight m subscript straight x space plus space straight m subscript straight y space equals space straight m rightwards double arrow space straight m subscript straight y over 7 plus straight m subscript straight y space equals space straight m rightwards double arrow space space space space space space fraction numerator 8 straight m subscript straight y over denominator 7 end fraction space equals space straight m rightwards double arrow space straight m subscript straight y space equals space 7 over 8 space straight m only space 1 divided by 8 space part space remain rightwards double arrow space 1 space rightwards arrow with straight T subscript begin inline style bevelled 1 half end style space space end subscript on top space space space 1 half space space rightwards arrow with straight T subscript begin inline style bevelled 1 half space space end style end subscript on top space 1 fourth rightwards arrow with straight T subscript begin inline style bevelled 1 half space space end style end subscript on top space 1 over 8
Therefore, time taken to become 1/8 unstable part
= 3 x T1/2
= 3 x 1.4 x 109
= 4.2 x 109 y

Some More Questions From Wave Optics Chapter

Mock Test Series

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation