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BITSAT 2016
Exam
BITSAT
Year
2016
Subject
Physics
Chapter
Nuclear Physics

BITSAT 2016 · Physics · Nuclear Physics

A radioactive element X converts into another stable element Y....

A radioactive element X converts into another stable element Y. Half life of X\mathrm{X} is 2hrs2 \mathrm{hrs}. Initially only X\mathrm{X} is present. After time t,\mathrm{t}, the ratio of atoms of XX and YY is found to be 1:4,1: 4, then tt in hours is

Options

  1. A2
  2. B4
  3. Cbetween 4 and 6
  4. D6

Correct answer

C. between 4 and 6

Step-by-step solution

Let N0\mathrm{N}_{0} be the number of atoms of X\mathrm{X} at time t=0\mathrm{t}=0 Then at t=4\mathrm{t}=4 hrs (two half lives) Nx=N04\mathrm{N}_{\mathrm{x}}=\frac{\mathrm{N}_{0}}{4} and Ny=3N04∴Nx/Ny=1/3\mathrm{N}_{\mathrm{y}}=\frac{3 \mathrm{ N}_{0}}{4}\therefore \mathrm{N}_{\mathrm{x}} / \mathrm{N}_{\mathrm{y}}=1 / 3 and at t=6hrs\mathrm{t}=6 \mathrm{hrs} (three half lives) Nx=N08\mathrm{N}_{\mathrm{x}}=\frac{\mathrm{N}_{0}}{8} and Ny=7N08\mathrm{N}_{\mathrm{y}}=\frac{7 \mathrm{ N}_{0}}{8} or NxNy=17\frac{\mathrm{N}_{\mathrm{x}}}{\mathrm{N}_{\mathrm{y}}}=\frac{1}{7} The given ratio 14\frac{1}{4} lies between 13\frac{1}{3} and 17\frac{1}{7} Therefore, t lies between 4hrs4 \mathrm{hrs} and 6hrs6 \mathrm{hrs}.
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