JEE Main · 2021 · 20 Jul 2021 · Shift 1 · Modern Physics

WhatsApp Email

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains? (Take

ln 3 = 1.1

)

(A)340 years
(B)1110 years
(C)700 years
(D)740 years✓ Correct

Answer: (D)

Solution

The two emissions proceed simultaneously and independently, so their decay constants add:

λ = \frac{ln 2}{1400} + \frac{ln 2}{700} = \frac{3 ln 2}{1400} y r^{- 1}

One third of the material is left when

e^{- λ t} = \frac{1}{3}

, that is when

λ t = ln 3

. Hence

t = \frac{1400 ln 3}{3 ln 2} = \frac{1400 \times 1.1}{3 \times 0.693} = 741 yr

The material falls to one third of its amount after about

740

years.

JEE Main · 2021 · 20 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 →