English

The half-life of radon is 3.82 d. By what time would 99.9% of radon will be decayed?

Advertisements
Advertisements

Question

The half-life of radon is 3.82 d. By what time would 99.9% of radon will be decayed?

Numerical
Advertisements

Solution

Given: t1/2 = 3.82 d, N0 = 100 N = 100 - 99.9 = 0.1

To find: t

Formulae: 

  1. `lambda = 0.693/"t"_(1//2)`
  2. t = `2.303/lambda log_10 ("N"_0/"N")`

Calculation: 

  1. `lambda = 0.693/"t"_(1//2) = 0.693/3.82 = 0.1814  "d"^-1`
  2. t = `2.303/lambda log_10 ("N"_0/"N")`
    `= 2.303/0.1814 xx log_10 (100/0.1)`
    `= 2.303/0.1814 log_10 (1000)`
    t = 38.087 d ≈ 38.1 d

Time taken for 99.9% of radon to be decayed is 38.1 d.

shaalaa.com
  Is there an error in this question or solution?
Chapter 13: Nuclear Chemistry and Radioactivity - Exercises [Page 203]

APPEARS IN

Balbharati Chemistry [English] Standard 11 Maharashtra State Board
Chapter 13 Nuclear Chemistry and Radioactivity
Exercises | Q 4. (K) | Page 203

RELATED QUESTIONS

What is gamma decay?


Describe alpha, beta and gamma decays and write down the formulae for the energies generated in each of these decays.


Complete the following equation describing nuclear decay.

\[\ce{_8^19O->e^- { +}}\] _____


Complete the following equation describing nuclear decay.

\[\ce{_90^228Th->\alpha { +}}\] _____


Choose the correct option.

\[\ce{^60_27CO}\] decays with a half-life of 5.27 years to produce \[\ce{^60_28Ni}\]. What is the decay constant for such radioactive disintegration?


Write relation between decay constant of a radioelement and its half-life.


Decay constant of 197Hg is 0.017 h-1. What is its half-life?


The half-life of 18F is 110 minutes. What fraction of 18F sample decays in 20 minutes?


The half-life of 67Ga is 78 h. How long will it take to decay 12% of the sample of Ga?


65% of 111In sample decays in 4.2 d. What is its half-life?


A sample of old wood shows 7.0 dps/g. If the fresh sample of tree shows 16.0 dps/g, how old is the given sample of wood? (Half-life of 14C is 5730 y)


Show that half life period of radioactive material varies inversely to decay constant λ.


Obtain an expression for the half-lifetime of radioactive material. Hence state the relation between an average life and half life time of radioactive material.


The activity of a radioactive sample ____________.


For radioactive substances, the fraction of its initial quantity (N0) which will disintegrate in its average lifetime is about ______.

(e = 2.71)


The activity of a radioactive substance decreases by a factor of 32 in one hour. The half-life of the substance (in min) is ______.


The disintegration rate of a radio-active sample is 1010 per hour at 20 hours from the start. It reduces to 5 × 109 per hour after 30 hours. Calculate the decay constant.


If the number of nuclei of a radioactive substance becomes `1/e` times the initial number in 10 days, what is the decay constant of the substance?


Show that the number of nuclei of a radioactive material decreases exponentially with time.


Define half-life period.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×