Calculation of Decayed / Undecayed Fractions of Radioactivity Class-12 Nootan ISC Physics Solution Ch-28. Step by step solutions of Kumar and Mittal Physics of Nageen Prakashan as council latest prescribe guideline for upcoming exam. Visit official Website CISCE for detail information about ISC Board Class-12 Physics.
Calculation of Decayed / Undecayed Fractions of Radioactivity Class-12 Nootan ISC Physics Solution Ch-28
| Class | 12 |
| Subject | Physics |
| Book | Nootan |
| Chapter-28 | Radioactivity |
| Topics | Numericals on Calculation of Decayed / Undecayed Fractions |
| Academic Session | 2025-2026 |
Numericals on Calculation of Decayed / Undecayed Fractions
Class-12 Nootan ISC Physics Solution Ch-28 Radioactivity
Que-1: The half-life of radium is 1600 years. What fraction of a sample of radium will be disintegrated after 6400 years?
Ans- Suppose that the original no. of radium is No then,
Que-2: The half-life of a radioactive nucleus is 3 minutes. What fraction of 1 g sample of this element will remain radioactive after 9 minutes?
Ans- Given,
Que-3: The half-life of radon is 3.8 days. In how many days will its activity drop to 6.25% of its initial value?
Ans- Given T1/2 = 3.8 Days
N = 6.25% of No
=> 6.25/100 x No
Suppose that the time is t then
Que-4: Accidently some radioactive material (half-life 10 days) spreads in a room. Tests show that the level of radiation is 32 times the permissible level. After how many days can the room be safe for living?
Ans- Given T1/2 = 10 Days
N = 1/32 No
Suppose that the rate of living time is t then
Que-5: Tritium (1H3) has a half-life of 12.5 years against beta decay. What fraction of a sample of pure tritium will remain undecayed after 25 years?
Ans- Given T1/2 = 12.5 years t = 25 years
Suppose that the initial value of tritium is No then
Therefore undecayed tritium is 1/4 parts
Que-6: What percentage of a radioactive material will be left undecayed after four half-lives?
Ans-
Que-7: Plutonium decays with a half-life of 24000 years. If it is stored for 72000 years, what fraction of it will remain?
Ans-
Que-8: The half-life of a radioactive substance is 30 days. What time will it take for (3/4)th of its original mass to disintegrate?
Ans-
Que-9: The half-life of strontium-90 is 30 years. will 0.04 g strontium-90 become 0.005 g after decay? In what time
Ans-
Que-10: After a certain lapse of time, the fraction of radioactive polonium undecayed is found to be 3.125% of its initial quantity. What is the duration of this time lapse if the half-life of polonium is 138 days?
Ans-
Que-11: 80 g of a radioactive material is allowed to decay for 15 days. The mass left undecayed after this period is 2.5 g. Calculate the half-life of the material.
Ans-
Que-12: 75% of a radioactive element disintegrates in 24 years. Calculate the half-life of the element.
Ans-
Que-13: The half-life of radium is 1550 years. Calculate its disintegration constant (λ). (ISC 2019)
Ans- We know that
Que-14: The half-life of a radioactive material is 60 years. After what time will it be reduced to one-sixteenth of its original mass? Calculate its decay constant also. (loge 2 = 0.693)
Ans-
Que-15: The decay constant of a radioactive material is 0.002 year^-1. Find its average life.
Ans- The average life
Que-16: A radioactive substance decays to (1/32) of its initial activity in 25 days. Calculate its half-life and decay constant.
Ans- Suppose that the half life is T1/2 and decay constant λ
Que-17: The half-life of a radioactive substance is 3 second. Initially it has 8000 atoms. Find (i) its decay constant and (ii) time after which 1000 atoms will remain undecayed.
Ans- Given T1/2 = 3 sec
No = 8000 Atoms
N = 1000 Atoms
Que-18: The half-life of a radioactive material is 24.1 days. How long will a sample take to decay 90% of it? (loge 2 = 0.6931)
Ans-
Que-19: 1.0 g of radium is reduced by 2.0 mg in 5 years by a-decay. Calculate the half-life of radium.
Ans- Given No = 1 gm
N = 1 g – 2 mg = 1.000 – 0.002 = 0.998 g
T1/2 = 5 years
Que-20: At a certain instant, a piece of radioactive material contains 10^12 atoms. The half-life of the material is 30 days.
(i) Find the number of disintegrations in the first second.
(ii) What time would elapse before 10^4 atoms remain?
(iii) What is the count rate after this time?
Ans- T1/2 = 30 Days , No = 10^12
We know that
λ = 0.6931/T1/2
=> 0.6931/30 = 0.0231 /Days
–: Calculation of Decayed / Undecayed Fractions of Radioactivity Class-12 Nootan ISC Physics Solution Ch-28 :–
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