The half life of a radioactive substance is 5 years. After x years, a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ______.
Correct Answer: 20
Solution and Explanation
The correct answer is 20
N = N0e–λt
\(⇒ \frac{6.25}{100} = e^{-λt}\)
\(⇒ e^{-λt} = \frac{1}{16} = (\frac{1}{2})^4\)
⇒ t = 4t1/2
⇒ t = 20 years
Top Questions on Radioactivity
- The half-life of radioactive isotope Zn$^{65}$ is 245 days. Find the time after which activity of Zn sample remains 75% of its initial value.
- JEE Main - 2026
- Chemistry
- Radioactivity
- The half-life of a radioactive substance is 4 hours. If initially there are 256 grams, how much remains after 10 hours?
- BITSAT - 2025
- Physics
- Radioactivity
- Write two properties of beta rays.
- Bihar Board XII - 2025
- Physics
- Radioactivity
- The half-life of a radioactive element is 10 minutes. Find the time in which its activity reduces to 1/16 of the original.
- The half life of a radioactive substance is 10 minutes. If $n_1$ and $n_2$ are the number of atoms decayed in 20 and 30 minutes respectively, then $n_1 : n_2 = $
- AP EAPCET - 2025
- Physics
- Radioactivity
Questions Asked in JEE Main exam
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$)
- JEE Main - 2026
- Rotational Mechanics
- If the coefficient of \( x \) in the expansion of \[ (ax^2 + bx + c)(1 - 2x)^{26} \] is \(-56\) and the coefficients of \( x^2 \) and \( x^3 \) are both zero, then \( a + b + c \) is equal to
- JEE Main - 2026
- Binomial theorem
The equivalent resistance between the points \(A\) and \(B\) in the given circuit is \[ \frac{x}{5}\,\Omega. \] Find the value of \(x\).
- JEE Main - 2026
- Current electricity
Method used for separation of mixture of products (B and C) obtained in the following reaction is:
- JEE Main - 2026
- p -Block Elements
- Consider light travelling from a medium A to medium B separated by a plane interface. If the light undergoes total internal reflection during its travel from medium A to B and the speed of light in media A and B are \(2.4 \times 10^8\) m/s and \(2.7 \times 10^8\) m/s, respectively, then the value of critical angle is :
- JEE Main - 2026
- Newtons Laws of Motion
Concepts Used:
Radioactivity
Radioactivity is a phenomenon observed in certain elements where unstable atomic nuclei spontaneously emit energy and subatomic particles. This process is driven by the desire of the nucleus to achieve a more stable state. It's crucial to understand the three main types of radioactive decay:
Alpha Decay: In alpha decay, a nucleus emits an alpha particle, consisting of two protons and two neutrons.
Beta Decay: Beta decay involves the emission of a beta particle, which can be a positron or an electron, from an unstable nucleus.
Gamma Decay: Gamma decay releases gamma rays, electromagnetic radiation, to achieve a more stable nuclear state.
The emission of these particles and energy is a result of nuclear instability. The rate of decay is characterized by the half-life, the time taken for half of the radioactive material to undergo decay. Radioactivity has diverse applications, from medical treatments and industrial processes to power generation in nuclear reactors.