Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.
Calculate the time interval between $33 \%$ decay and $67 \%$ decay if half-life of a substance is 20 minutes.
60 minutes
20 minutes
40 minutes
13 minutes
Correct Option: 2,
$\mathrm{N}_{1}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}_{1}}$
$\frac{\mathrm{N}_{1}}{\mathrm{~N}_{0}}=\mathrm{e}^{-\lambda \mathrm{t}_{1}}$
$0.67=\mathrm{e}^{-\lambda t_{1}}$
$\ln (0.67)=-\lambda t_{1}$
$\mathrm{N}_{2}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}_{2}}$
$\frac{\mathrm{N}_{2}}{\mathrm{~N}_{0}}=\mathrm{e}^{-\lambda \mathrm{t}_{2}}$
$0.33=e^{-\lambda t_{2}}$
$\ln (0.33)=-\lambda t_{2}$
$\ln (0.67)-\ln (0.33)=\lambda t_{1}-\lambda t_{2}$
$\lambda\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right)=\ln \left(\frac{0.67}{0.33}\right)$
$\lambda\left(\mathrm{t}_{1}-\mathrm{t}_{2}\right) \cong \ln 2$
$\mathrm{t}_{1}-\mathrm{t}_{2} \simeq \frac{\ln 2}{\lambda}=\mathrm{t}_{1 / 2}$
Half life $=\mathrm{t}_{1 / 2}=20$ minutes.
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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,