A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decays in 100 years, then what is the decay constant (proportionality constant) ?

This question was previously asked in
NDA 01/2022: Maths Previous Year paper (Held On 10 April 2022)
View all NDA Papers >
  1. \(\frac{\ln 2}{100}\)
  2. \(\frac{\ln 5}{100}\)
  3. \(\frac{\ln 10}{100}\)
  4. \(\frac{2 \ln 2}{100}\)

Answer (Detailed Solution Below)

Option 1 : \(\frac{\ln 2}{100}\)
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
6 K Users
150 Questions 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

Concept

Half-life:  \(\displaystyle t_{\frac{1}{2}}=\frac{log_e2}{k}\)

Where k is the decay constant.

Calculation:

We know that  \(\displaystyle t_{\frac{1}{2}}=\frac{log_e2}{k}\)

Putting the value of t1/2 = 100 years,

⇒ 100 = \(\displaystyle \frac{log_e2}{k}\)

⇒ k = \(\displaystyle \frac{log_e2}{100}\)

∴ Decay constant is \(\displaystyle \frac{log_e2}{100}\).

Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Get Free Access Now
Hot Links: teen patti customer care number teen patti gold download apk mpl teen patti teen patti master online teen patti mastar