Home
Class 12
MATHS
A certain radioactive material is known ...

A certain radioactive material is known to decay at a rate proportional to the amount present. Initially there is 50 kg of the material present and after 2h it is observed that the material has lost 10 percent of its original mass. Based on these data answer the following questions.
The time at which the material has decayed to one half of its initial mass is

A

`50^(-0.5" ln "9)`

B

`50e^(-2" ln "9)`

C

`50e^(-2" ln "0.9)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
We require N at t=4. Substituting t=4 into (3) and then solving for N, we find
`N=50e^(2" ln "0.9)`
Promotional Banner

Topper's Solved these Questions

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Numerical value type|17 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise Archives|12 Videos

  • DIFFERENTIAL EQUATIONS

    CENGAGE ENGLISH|Exercise MULTIPLE CORRECT ANSWERS TYPE|17 Videos

  • DIFFERENT PRODUCTS OF VECTORS AND THEIR GEOMETRICAL APPLICATIONS

    CENGAGE ENGLISH|Exercise Multiple correct answers type|11 Videos

  • DIFFERENTIATION

    CENGAGE ENGLISH|Exercise Archives|14 Videos

Similar Questions

Explore conceptually related problems

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 kg of the material present and after two hours it is observed that the material has lost 10% of its original mass, find () and expression for the mass of the material remaining at any time t, (ii) the mass of the material after four hours and (iii) the time at which the material has decayed to one half of its initial mass.

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 kg of the material present and after two hours it is observed that the material has lost 10% of its original mass, find () and expression for the mass of the material remaining at any time t, (ii) the mass of the material after four hours and (iii) the time at which the material has decayed to one half of its initial mass.

A certain radioactive element has half-life of 4 days. The fraction of material that decays in 2 days is

A radioactive material decays by simulataneous emission of two particle from the with respective half - lives 1620 and 810 year . The time , in year , after which one - fourth of the material remains is

A radioactive material decays by simultaneous emission of two particle from the with respective half - lives 1620 and 810 year . The time , in year , after which one - fourth of the material remains is

Consider a situation where a cart carrying five boys is moving without friction due to inertia along a straight horizontal road, with a speed of 10 m/s. After travelling certain distance a boy jumps from the cart with a speed of 2 m/s with respect to cart in opposite direction to it. Then, second boy jumps with the same speed w.r.t. the cart, but in a perpendicular direction to the cart. The mass of the cart is 100 kg and mass of each boy is 20 kg. Answer the following questions. The speed of the cart after first boy has jumped out is

A block of mass m is connected to a spring of spring constant k as shown in Fig. The block is found at its equilibrium position t=1s and it has a velocity of +0.25(m)/(s) at t=2s . The time period of oscillation is 6 s. Based on the given information answer the following question: Q. the amplitude of oscillation is

A block of mass m is connected to a spring of spring constant k as shown in Fig. The block is found at its equilibrium position t=1s and it has a velocity of +0.25(m)/(s) at t=2s . The time period of oscillation is 6 s. Based on the given information answer the following question: Q. Determine the velocity of particle at t=5s .

Radioactive material 'A' has decay constant '8 lamda' and material 'B' has decay constant 'lamda'. Initial they have same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be (1)/( e) ?

Radioactive material 'A' has decay constant '8 lamda' and material 'B' has decay constant 'lamda'. Initial they have same number of nuclei. After what time, the ratio of number of nuclei of material 'A' to that 'B' will be '(1/ e) ?

CENGAGE ENGLISH-DIFFERENTIAL EQUATIONS-Linked Comprehension types
  1. For certain curve y=f(x) satisfying (d^(2)y)/(dx^(2))=6x-4, f(x) has l...

    Text Solution

    |

  2. For certain curve y=f(x) satisfying (d^(2)y)/(dx^(2))=6x-4, f(x) has l...

    Text Solution

    |

  3. The differential equation y=px+f(p), …………..(i) where p=(dy)/(dx),is k...

    Text Solution

    |

  4. The differential equation y=px+f(p), …………..(i) where p=(dy)/(dx),is ...

    Text Solution

    |

  5. The differential equation y=px+f(p), …………..(i) where p=(dy)/(dx),is ...

    Text Solution

    |

  6. Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...

    Text Solution

    |

  7. Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...

    Text Solution

    |

  8. Let f(x) be a non-positive continuous function and F(x)=int(0)^(x)f(t)...

    Text Solution

    |

  9. A curve C with negative slope through the point (0, 1) lies in the fir...

    Text Solution

    |

  10. A curve 'C' with negative slope through the point(0,1) lies in the I Q...

    Text Solution

    |

  11. A curve C with negative slope through the point (0, 1) lies in the fir...

    Text Solution

    |

  12. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x-int(0)...

    Text Solution

    |

  13. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int(0...

    Text Solution

    |

  14. Let y=f(x) satisfies the equation f(x) = (e^(-x)+e^(x))cosx-2x+int(0...

    Text Solution

    |

  15. A certain radioactive material is known to decay at a rate proportiona...

    Text Solution

    |

  16. A certain radioactive material is known to decay at a rate proportiona...

    Text Solution

    |

  17. A certain radioactive material is known to decay at a rate proportiona...

    Text Solution

    |

  18. Consider a tank which initially holds V(0) liter of brine that contain...

    Text Solution

    |

  19. A 50 L tank initailly contains 10 L of fresh water, At t=0, a brine so...

    Text Solution

    |

  20. In the above question, the amount of salt in the tank at the moment of...

    Text Solution

    |