JEE Main · 2019 · 12 Apr 2019 · Shift 2 · Modern Physics

Half lives of two radioactive nuclei

A

and

B

are 10 minutes and 20 minutes, respectively. If, initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei

A

and

B

will be :

(A) $9 : 8$ ✓ Correct
(B) $1 : 8$
(C) $8 : 1$
(D) $3 : 8$

Answer: (A)

Solution

After

60

minutes nucleus

A

has passed

\frac{60}{10} = 6

half-lives, leaving

\frac{N _{0}}{64}

, so the decayed amount is

\frac{63 N _{0}}{64}

. Nucleus

B

has passed

\frac{60}{20} = 3

half-lives, leaving

\frac{N _{0}}{8}

, so it has lost

\frac{7 N _{0}}{8}

. The ratio of decayed numbers is

\frac{63/64}{7/8} = \frac{63}{64} \times \frac{8}{7} = \frac{9}{8}

, that is

9 : 8

JEE Main · 2019 · 12 Apr 2019 · Shift 2 · 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 →