A radio-active material is reduced to 1/8 of its original amount in 3 days. If $8 \times 10^{-3} \mathrm{~kg}$ of the material is left after 5 days. The initial amount of the material is

JEE Main · 2023 · 08 Apr 2023 · Shift 2 · Modern Physics

A radio-active material is reduced to 1/8 of its original amount in 3 days. If

8 \times 1 0^{- 3} kg

of the material is left after 5 days. The initial amount of the material is

(A)64 g
(B)40 g
(C)32 g
(D)256 g✓ Correct

Answer: (D)

Solution

Using the radioactive decay formula

N = N_{0} (\frac{1}{2})^{n}

. Given that the material reduces to 1/8 in 3 days:

\frac{N _{0}}{8} = N_{0} (\frac{1}{2})^{n}

gives

n = 3

half-lives. So 3 half-lives = 3 days, meaning 1 half-life = 1 day. After 5 days (5 half-lives):

8 \times 1 0^{- 3} = N_{0} (\frac{1}{2})^{5} = \frac{N _{0}}{32}

. Therefore

N_{0} = 8 \times 1 0^{- 3} \times 32 = 256 \times 1 0^{- 3}

kg = 256 g.

JEE Main · 2023 · 08 Apr 2023 · 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 →