JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Modern Physics

If '

f

' denotes the ratio of the number of nuclei decayed (

N_{d}

) to the number of nuclei at

t = 0

(

N_{0}

) then for a collection of radioactive nuclei, the rate of change of '

f

' with respect to time is given as: [

λ

is the radioactive decay constant]

(A) $λ e^{- λ t}$ ✓ Correct
(B) $λ (1 - e^{- λ t})$
(C) $- λ (1 - e^{- λ t})$
(D) $- λ e^{- λ t}$

Answer: (A)

Solution

The fraction of nuclei decayed is

f = \frac{N _{0} - N}{N _{0}} = 1 - e^{- λ t}

. Taking the derivative with respect to time:

\frac{df}{d t} = 0 - e^{- λ t} \times (- λ) = λ e^{- λ t}

JEE Main · 2021 · 27 Jul 2021 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Modern Physics →

More JEE Main questions on Modern Physics

7.9 MeV α-particle scatters from a target material of atomic number 79. From the given data the estimated diameter of nuclei of the target material is (approximately) ______ m.
[ $\frac{1}{4 π ϵ _{0}} = 9 \times 1 0^{9}$ Nm²/C² and electron charge $= 1.6 \times 1 0^{- 19}$ C]
JEE Main 2026View solution →
The minimum frequency of photon required to break a particle of mass 15.348 amu into $4 α$ particles is ______ kHz.
[mass of He nucleus = 4.002 amu, $1$ amu $= 1.66 \times 1 0^{- 27}$ kg, $h = 6.6 \times 1 0^{- 34}$ J.s and $c = 3 \times 1 0^{8}$ m/s]
JEE Main 2026View solution →
The smallest wavelength of Lyman series is 91 nm. The difference between the largest wavelengths of Paschen and Balmer series is nearly $____$ nm.
JEE Main 2026View solution →
Light is incident on a metallic plate having work function $110 \times 1 0^{- 20} J$ . If the produced photoelectrons have zero kinetic energy then the angular frequency of the incident light is ______ $rad / s$ . ( …
JEE Main 2026View solution →
The energy of an electron in an orbit of the Bohr's atom is $- 0.04 E_{0} eV$ where $E_{0}$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then …
JEE Main 2026View solution →
A particle having electric charge $3 \times 1 0^{- 19} C$ and mass $6 \times 1 0^{- 27} kg$ is accelerated by applying an electric potential of 1.21 V . Wavelength of the matter wave associated with the particle is $α \times 1 0^{- 12} m$ . The va …
JEE Main 2026View solution →