Verified Solution • 2025–26 Session moderate

QJEEM03Chaf6c: JEE Main 2003 Chemistry - Class 12 JEEM03Chaf6c Solution: The half-life of a radioactive isotope is three hours. If the…

The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were 256 g, the mass of it remaining undecayed after 18 hours would be

Multiple Choice Options

  • A 8.0 g
  • B 12.0 g
  • C 16.0 g
  • D 4.0 g

Step-by-Step Verified Solution

t1/2=3 {t_{1/2}} = 3\, hrs. T=18T=18 hours

as     T=n×t1/2\,\,\,\,T = n \times {t_{1/2}}

∴\therefore     n=183=6\,\,\,\,n = {{18} \over 3} = 6

Initial mass (C0)=256 g\left( {{C_0}} \right) = 256\,g

∴\therefore     Cn=C02n=256(2)6=25664=4g.\,\,\,\,{C_n} = {{{C_0}} \over {{2^n}}} = {{256} \over {{{\left( 2 \right)}^6}}} = {{256} \over {64}} = 4g.

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