If ' $f$ ' denotes the ratio of the number of nuclei decayed $\left(\mathrm{N}_{\mathrm{d}}\right)$ to the number of nuclei at $t=0\left(\mathrm{~N}_{0}\right)$ then for a collection of radioactive nuclei, the rate of change of ' $f$ ' with respect to time is given as :
$[\lambda$ is the radioactive decay constant]
$-\lambda\left(1-e^{-\lambda t}\right)$
$\lambda\left(1-e^{-\lambda t}\right)$
$\lambda \mathrm{e}^{-\lambda \mathrm{t}}$
$-\lambda \mathrm{e}^{-\lambda t}$
Correct Option: , 3
$\mathrm{N}=\mathrm{N}_{0} \mathrm{e}^{-\lambda \mathrm{t}}$
$\mathrm{N}_{\mathrm{d}}=\mathrm{N}_{0}-\mathrm{N}$
$\mathrm{N}_{\mathrm{d}}=\mathrm{N}_{0}\left(1-\mathrm{e}^{-\lambda \mathrm{t}}\right)$
$\frac{N_{d}}{N_{0}}=f=1-e^{-\lambda . t}$
$\frac{\mathrm{df}}{\mathrm{dt}}=\lambda \mathrm{e}^{-\lambda t}$
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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,