MHT CET · Physics · Nuclear Physics
A radioactive sample has half-life of 5 years. The percentage of fraction decayed in 10 years will be
- A \(25 \%\)
- B \(50 \%\)
- C \(75 \%\)
- D \(100 \%\)
Answer & Solution
Correct Answer
(C) \(75 \%\)
Step-by-step Solution
Detailed explanation
Given:
Total time, \(\mathrm{T}=10\) years
Half life, \(\mathrm{T}_{1 / 2}=5\) years
\(\therefore \quad\) No. of half lives, \(\mathrm{n}=\frac{10}{5}=2\)
From \(\frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^{\mathrm{n}}\)
\(\therefore \quad \frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^2=\frac{1}{4}\)
\(\therefore \quad\) After 10 years, \(\frac{1}{4}^{\text {th }}\) of the original substance will remain.
\(\Rightarrow\left(1-\frac{1}{4}\right)=\frac{3}{4} \times 100=75 \%\) of the fraction would get decayed.
Total time, \(\mathrm{T}=10\) years
Half life, \(\mathrm{T}_{1 / 2}=5\) years
\(\therefore \quad\) No. of half lives, \(\mathrm{n}=\frac{10}{5}=2\)
From \(\frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^{\mathrm{n}}\)
\(\therefore \quad \frac{\mathrm{N}}{\mathrm{N}_0}=\left(\frac{1}{2}\right)^2=\frac{1}{4}\)
\(\therefore \quad\) After 10 years, \(\frac{1}{4}^{\text {th }}\) of the original substance will remain.
\(\Rightarrow\left(1-\frac{1}{4}\right)=\frac{3}{4} \times 100=75 \%\) of the fraction would get decayed.
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- In photoelectric effect, the kinetic energy of electron emitted from the metal surface depends uponMHT CET 2022 Easy
- Two identical parallel plate air capacitors are connected in series to a battery of emf V. If one of the capacitor is completely filled with dielectric material of constant K, then potential difference of the other capacitor will becomeMHT CET 2016 Medium
- Three parallel plate air capacitors are connected in parallel. Each capacitor has plate area \(\frac{A}{3}\) and the separation between the plates is \(d, 2 d\) and \(3 d\) respectively. The equivalent capacity of combination is ( \(\varepsilon_0=\) absolute permittivity of free space)MHT CET 2016 Easy
- When a charge of \(3 \mathrm{C}\) is placed in uniform electric field, it experiences a force of \(3000 \mathrm{~N}\). Within this field, potential difference between two points separated by a distance of \(1 \mathrm{~cm}\) isMHT CET 2023 Medium
- A thick brass wire of length ' \(\mathrm{L}\) ' and density ' \(\rho\) ' is suspended from rigid support.
Due to its own weight, \(' \ell^{\prime}\) is the increase in length. Young's modulus ' \(\mathrm{Y}^{\prime}\) of brass
wire in terms of density is
\((\mathrm{g}=\) acceleration due to gravity \()\)MHT CET 2020 Easy - Inside a bar magnet, the magnetic lines of forceMHT CET 2020 Easy
More PYQs from MHT CET
- Which among the following carbohydrates is a trisaccharide?MHT CET 2021 Medium
- In neural system, chemical synapse shows synaptic gap of about ___________ .MHT CET 2021 Easy
- Which of the following methods is used to separate wolframite and stannic oxide present in cassiterite?MHT CET 2019 Medium
- If \(\frac{x^2}{a^2}+\frac{\mathrm{y}^2}{\mathrm{~b}^2}=1\), then \(\frac{\mathrm{d}^2 \mathrm{y}}{\mathrm{d} x^2}\) isMHT CET 2025 Medium
- Calculate the molar mass of an element if it forms fcc unit cell structure
[mass of unit cell \(=1.8 \times 10^{-22} \mathrm{~g}, \mathrm{~N}_{\mathrm{A}}=6.022 \times 10^{23} \mathrm{~mol}^{-1}\) ]MHT CET 2025 Hard - The equivalent resistance of the following circuit when no current flows in the resistance of \(5 \Omega\) is nearly
MHT CET 2025 Medium