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 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
- Given: \[ \frac{197}{96} X \to \frac{197}{95} Y + Z + V \quad \text{what is Z?} \]
- KEAM - 2025
- Physics
- Radioactivity
Questions Asked in JEE Main exam
- Number of solutions of the equation \[ \sqrt{3} \cos 2\theta + 8 \cos \theta + 3\sqrt{3} = 0 \] in \( \theta \in \left[ -3\pi, 2\pi \right] \):
- JEE Main - 2026
- Trigonometric Equations
The following diagram shows a Zener diode as a voltage regulator. The Zener diode is rated at \(V_z = 5\) V and the desired current in load is 5 mA. The unregulated voltage source can supply up to 25 V. Considering the Zener diode can withstand four times of the load current, the value of resistor \(R_s\) (shown in circuit) should be_______ \(\Omega\).
- JEE Main - 2026
- Current electricity
Two point charges 2q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is :
- JEE Main - 2026
- Rotational motion
- The speed of a longitudinal wave in a metallic bar is \(400\,\text{m/s}\). If the density and Young’s modulus of the bar material increase by \(0.5%\) and \(1%\) respectively, then the speed of the wave is changed approximately to _______ m/s.
- JEE Main - 2026
- General Physics
\[ \left( \frac{1}{{}^{15}C_0} + \frac{1}{{}^{15}C_1} \right) \left( \frac{1}{{}^{15}C_1} + \frac{1}{{}^{15}C_2} \right) \cdots \left( \frac{1}{{}^{15}C_{12}} + \frac{1}{{}^{15}C_{13}} \right) = \frac{\alpha^{13}}{{}^{14}C_0 \, {}^{14}C_1 \cdots {}^{14}C_{12}} \]
Then \[ 30\alpha = \underline{\hspace{1cm}} \]
- JEE Main - 2026
- Binomial theorem
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.