
If the half-life of radium is\[7\] days. Its decay constant in a day will be
A. \[3 \times 10^{ - 13}\] /day
B. \[9 \times 10^{ - 3}\] /day
C. \[1 \times 10^{ - 3}\] /day
D .\[6 \times 10^{ - 6}\] /day
Answer
162.3k+ views
Hint: Decay constant is also known as disintegration constant. It is ratio of number of radioactive atoms disintegrating in a short interval of time to the number of atoms of same kind present at the starting. It is represented by the symbol\[\lambda\]. Decay constant unit is\[\delta ^{ - 1}\]. It is the inverse of decay time.
The half-life\[( T_{1/2} )\] for a radioisotope is the time taken to decay nuclei of a radioactive sample to half of its initial number of nuclei. The half-life of radioactive decay is inversely proportional to the decay constant.
Formula Used:In this solution we will be using the following formulae, \[\begin{array}{l}\lambda =\dfrac{0.693}{T_{1/2}} \end{array}\]
where \[( T_{1/2} )\] is the half-life of radioactive atoms and\[( \lambda )\]is the decay constant.
Decay constant\[( \lambda )\] is the fraction of total nuclei that will decay per unit of time \[( t ) \].
Complete step by step solution:Radioactive elements are made up of atoms. The emitting radiation transforms radioactive atoms into another chemical element. It may be stable or maybe radioactive. Then it undergoes further decay.
The time interval required for one-half of the atomic nuclei of a radioactive sample decay. Half-life, in radioactivity, is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.
The first-order reaction in the half-life is a constant. It is related to the rate constant for the reaction. Where $( T_{1/2} )$ is half-life and $( \lambda )$ is the decay constant. It is given that the half-life of given substances is \[7\] .
Now, comes the solution;\[\lambda =\dfrac{0.693}{T_{1/2}}\]
Where half-life $( T_{1/2} )$is given that i\[7\] . We can get \[\lambda =\dfrac{0.693}{77}\] \[ =\]\[0.00\]\[ =\]\[9 \times 10^{ - 3}\] /day
That is the decay of the day will be \[9 \times 10^{ - 3}\]
option B is the correct answer
Note: The radioactive decay law and the half-life formula are used to find the age of organic material, which is known as radioactive dating. By knowing the half-life of radium i \[7\] days, the decay constant can be calculated directly by using the decay relation.
The half-life\[( T_{1/2} )\] for a radioisotope is the time taken to decay nuclei of a radioactive sample to half of its initial number of nuclei. The half-life of radioactive decay is inversely proportional to the decay constant.
Formula Used:In this solution we will be using the following formulae, \[\begin{array}{l}\lambda =\dfrac{0.693}{T_{1/2}} \end{array}\]
where \[( T_{1/2} )\] is the half-life of radioactive atoms and\[( \lambda )\]is the decay constant.
Decay constant\[( \lambda )\] is the fraction of total nuclei that will decay per unit of time \[( t ) \].
Complete step by step solution:Radioactive elements are made up of atoms. The emitting radiation transforms radioactive atoms into another chemical element. It may be stable or maybe radioactive. Then it undergoes further decay.
The time interval required for one-half of the atomic nuclei of a radioactive sample decay. Half-life, in radioactivity, is the interval of time required for one-half of the atomic nuclei of a radioactive sample to decay.
The first-order reaction in the half-life is a constant. It is related to the rate constant for the reaction. Where $( T_{1/2} )$ is half-life and $( \lambda )$ is the decay constant. It is given that the half-life of given substances is \[7\] .
Now, comes the solution;\[\lambda =\dfrac{0.693}{T_{1/2}}\]
Where half-life $( T_{1/2} )$is given that i\[7\] . We can get \[\lambda =\dfrac{0.693}{77}\] \[ =\]\[0.00\]\[ =\]\[9 \times 10^{ - 3}\] /day
That is the decay of the day will be \[9 \times 10^{ - 3}\]
option B is the correct answer
Note: The radioactive decay law and the half-life formula are used to find the age of organic material, which is known as radioactive dating. By knowing the half-life of radium i \[7\] days, the decay constant can be calculated directly by using the decay relation.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main Mock Test Series Class 12 Chemistry for FREE

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Classification of Drugs

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

Other Pages
NCERT Solutions for Class 12 Chemistry Chapter 1 Solutions

JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

Solutions Class 12 Notes: CBSE Chemistry Chapter 1

NCERT Solutions for Class 12 Chemistry Chapter 6 Haloalkanes and Haloarenes

NCERT Solutions for Class 12 Chemistry Chapter 2 Electrochemistry

Electrochemistry Class 12 Notes: CBSE Chemistry Chapter 2
