Question:
Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :
(where $\lambda$ is the decay constant)
$\frac{1}{2} \frac{\ln 2}{\lambda}$
$\frac{\ln 2}{\lambda}$
$\frac{2 \ln 2}{\lambda}$
$\frac{\ln \frac{3}{2}}{\lambda}$
Correct Option: , 4
Solution:
$\frac{3 \mathrm{~N}_{0}}{4}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}_{1}}$
$\frac{\mathrm{N}_{0}}{2}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}_{2}}$
$\ln (3 / 4)=-\lambda t_{1} \ldots . .$ (i)
$\ln (1 / 2)=-\lambda t_{2} \quad \ldots .$ (i)
$\ln (3 / 4)-\ln (1 / 2)=\lambda\left(t_{2}-t_{1}\right) \quad \ldots .$ (i)
$\Delta \mathrm{t}=\frac{\ln (3 / 2)}{\lambda}$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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