Question:
The activity of a radioactive material is 2.56 × 10–3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 × 10–5 Ci?
The activity of a radioactive material is 2.56 × 10–3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 × 10–5 Ci?
Updated On: Jul 8, 2024
- 30 days
- 35 days
- 40 days
- 25 days
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is( B): 35 days.
\(A=A_{0}e^{-λt}\)
⇒ 2 × 10–5 = 2.56 × 10–3e–λt
\(⇒e^{-λt}=\frac{1}{128}=[\frac{1}{2}]^7\)
\(⇒t=7t_{\frac{1}{2}}=35\,days\)
Was this answer helpful?
0
0
Top Questions on Escape Speed
- An object is kept at rest at a distance of 3R above the earth’s surface where $ R $ is earth’s radius. The minimum speed with which it must be projected so that it does not return to earth is: (Assume $ M $ = mass of earth, $ G $ = Universal gravitational constant)
- JEE Main - 2025
- Physics
- Escape Speed
- The escape velocity from the surface of a planet is 11.2 km/s. If the radius of the planet is doubled but the mass remains the same, what will be the new escape velocity?
- BITSAT - 2025
- Physics
- Escape Speed
- Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height ℎ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are t1 and t2, respectively. If \(H = ( \frac{16}{ 9} ) ℎ\), then the ratio t1/t2 is ___
- JEE Advanced - 2024
- Physics
- Escape Speed
- To project a body of mass \( m \) from Earth's surface to infinity, the required kinetic energy is (assume, the radius of Earth is \( R_E \), \( g \) = acceleration due to gravity on the surface of Earth):
- JEE Main - 2024
- Physics
- Escape Speed
- The mass of the moon is 1/144 times the mass of a planet and its diameter 1/16 times the diameter of a planet. If the escape velocity on the planet is v, the escape velocity on the moon will be:
- JEE Main - 2024
- Physics
- Escape Speed
View More Questions
Questions Asked in JEE Main exam
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.- JEE Main - 2026
- Complex Numbers and Quadratic Equations
- The work functions of two metals ($M_A$ and $M_B$) are in the 1 : 2 ratio. When these metals are exposed to photons of energy 6 eV, the kinetic energy of liberated electrons of $M_A$ : $M_B$ is in the ratio of 2.642 : 1. The work functions (in eV) of $M_A$ and $M_B$ are respectively.
- JEE Main - 2026
- Dual nature of matter
- 10 mole of an ideal gas is undergoing the process shown in the figure. The heat involved in the process from \( P_1 \) to \( P_2 \) is \( \alpha \) Joule \((P_1 = 21.7 \text{ Pa}, P_2 = 30 \text{ Pa}, C_v = 21 \text{ J/K mol}, R = 8.3 \text{ J/mol K})\). The value of \( \alpha \) is ________.
- JEE Main - 2026
- Thermodynamics
- The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has- JEE Main - 2026
- Matrices and Determinants
- The displacement of a particle executing simple harmonic motion with time period \(T\) is expressed as \[ x(t)=A\sin\omega t, \] where \(A\) is the amplitude of oscillation. If the maximum value of the potential energy of the oscillator is found at \[ t=\frac{T}{2\beta}, \] then the value of \(\beta\) is ________.
- JEE Main - 2026
- Waves and Oscillations
View More Questions
Concepts Used:
Speed and Velocity
The rate at which an object covers a certain distance is commonly known as speed.
The rate at which an object changes position in a certain direction is called velocity.
Difference Between Speed and Velocity:
Read More: Difference Between Speed and Velocity