MHT CET · Physics · Nuclear Physics
Activity of a radioactive sample decreases to \(\left(\frac{1}{3}\right)^{r d}\) of its original value in 3 days. Then in 9 days its activity reduces to
- A \(\left(\frac{1}{18}\right)\) of the original value
- B \(\left(\frac{1}{9}\right)\) of the original value
- C \(\left(\frac{1}{27}\right)\) of the original value
- D \(\left(\frac{1}{3}\right)\) of the original value
Answer & Solution
Correct Answer
(C) \(\left(\frac{1}{27}\right)\) of the original value
Step-by-step Solution
Detailed explanation
Activity after time \(t\) given that half-life is \(T\) :
\(A=\frac{A_0}{2^{t / T}}\)
\(\frac{A_0}{3}=\frac{A_0}{2^{3 / T}}\)
Activity in 9 days,
\(A=\frac{A_0}{2^{t / T}}=\frac{A_0}{2^{9 / T}}=\frac{A_0}{\left(2^{3 / T}\right)^3}=\frac{A_0}{27}\)
\(A=\frac{A_0}{2^{t / T}}\)
\(\frac{A_0}{3}=\frac{A_0}{2^{3 / T}}\)
Activity in 9 days,
\(A=\frac{A_0}{2^{t / T}}=\frac{A_0}{2^{9 / T}}=\frac{A_0}{\left(2^{3 / T}\right)^3}=\frac{A_0}{27}\)
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
- Two identical blocks each of mass ' \(M\) ' attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. A small mass ' \(m\) ' is now placed on the block B. The acceleration with which the two blocks move together is
[ \(\mathrm{g}=\) gravitational acceleration]
MHT CET 2024 Medium - On increasing the reverse bias to a large value in a P-N junction diode, currentMHT CET 2023 Easy
- The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by , keeping the length constant. The frequency of the wire isMHT CET 2019 Medium
- Three solid spheres each of mass ' \(M\) ' and radius ' \(R\) ' are arranged as shown in the figure. The moment of inertia of the system about YY' will be
MHT CET 2021 Medium - A coil is wound on a core of rectangular cross-section. If all the linear dimensions of core are increased by a factor 3 and number of turns per unit length of coil remains same, the self-inductance increases by a factorMHT CET 2025 Medium
- The magnetic flux through a circuit of resistance ' \(R\) ' changes by an amount \(\Delta \phi\) in the time \(\Delta t\). The total quantity of electric charge ' \(Q\) ' which passes during this time through any point of the circuit isMHT CET 2023 Medium
More PYQs from MHT CET
- In Young's double slit experiment let 'd' be the distance between two slits and 'D' be the distance between the slits and the screen. Using a monochromatic source of wavelength ' \(\lambda\) ', in an interference pattern, third minimum is observed exactly in front of one of the slits. If at the same point on the screen first minimum is to be obtained, the required change in the wavelength is [d & D are not changed]MHT CET 2025 Medium
- Which of the following compound is not aromatic?MHT CET 2012 Medium
- The decreasing order of bond angle in the following molecules isMHT CET 2022 Medium
- The first overtone of the vibrating air column of a closed pipe has the same frequency as the second overtone of an open pipe \(1.5 \mathrm{~m}\) Jung. The length of the closed pipe isMHT CET 2022 Medium
- Benzonitrile on reduction with stannous chloride in presence of hydrochloric acid followed by acid hydrolysis forms,MHT CET 2025 Easy
- The remnant of the embryonic aperture on the inter-auricular septum is called ____________ .MHT CET 2021 Medium