JEE Mains · Physics · STD 12 - 13. Nuclei
Half-lives of two radioactive elements \(A\) and \(B\) are \(20\) minutes and \(40\) minutes, respectively. Initially, the samples have equal number of nuclei. After \(80\) minutes, the ratio of decayed number of \(A\) and \(B\) nuclei will be
- A \(1 : 4\)
- B \(5 : 4\)
- C \(1 : 16\)
- D \(4 : 1\)
Answer & Solution
Correct Answer
(B) \(5 : 4\)
Step-by-step Solution
Detailed explanation
For \(A_{t / 2}=20\, min\), \(t=80\,min\), number of half lifes \(n=4\) \(\therefore \) Nuclei remaining \(=\frac{\mathrm{N}_{\mathrm{o}}}{2^{4}} .\) Therefore nuclei decayed \(=\mathrm{N}_{0}-\frac{\mathrm{N}_{0}}{2^{4}}\) For…
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
- A particle executes simple harmonic motion. Its amplitude is \(8 \,cm\) and time period is \(6 \,s\). The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ............. \(s\)JEE Mains 2022 Medium
- The relative error in the determination of the surface area of a sphere is \(\alpha \). Then the relative error in the determination of its volume isJEE Mains 2018 Hard
- A slit of width \(a\) is illuminated by light of wavelength \(\lambda\). The linear separation between \(1^{st}\) and \(3^{rd}\) minima in the diffraction pattern produced on a screen placed at a distance \(D\) from the slit system is _____.JEE Mains 2026 Medium
- An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at \(x =+2\,m\), its velocity is \(-4 \hat{ j }\, m / s\). The object's velocity \((v)\) and acceleration \((a)\) at \(x =-2\,m\) will beJEE Mains 2023 Medium
- Which of the following pair of nuclei are isobars of the element?JEE Mains 2026 Easy
- Given below are two statements:
Statement I: An object moves from position \( r_{1} \) to position \( r_{2} \) under a conservative force field \( \vec{F} \). The work done by the force is \( W=-\int_{r_{1}}^{r_{2}}\vec{F}\cdot d\vec{r} \).
Statement II Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force.
In the light of above statement, choose the correct answer from the options given below:JEE Mains 2026 Medium
More PYQs from JEE Mains
- Two identical strings \(X\) and \(Z\) made of same material have tension \(T _{ x }\) and \(T _{ z }\) in them. If their fundamental frequencies are \(450\, Hz\) and \(300\, Hz ,\) respectively, then the ratio \(T _{ x } / T _{ z }\) is\(.....\)JEE Mains 2020 Easy
- In the figure given, the electric current flowing through the \(5\, k \Omega\) resistor is \('x' mA.\) The value of \(x\) to the nearest integer is .........
JEE Mains 2021 Medium - A disc with a flat small bottom beaker placed on it at a distance \(R\) from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity \(\omega\). The coefficient of static friction between the bottom of the beaker and the surface of the disc is \(\mu\). The beaker will revolve with the disc ifJEE Mains 2022 Medium
- Let \(f(x)=\left\{\begin{array}{cc}-2, & -2 \leq x \leq 0 \\ x-2, & 0 < x \leq 2\end{array}\right.\) and \(h(x)=f(|x|)+|f(x)|\). Then \(\int_{-2}^2 \mathrm{~h}(\mathrm{x}) \mathrm{dx}\) is equal to :JEE Mains 2024 Hard
- If each term of a geometric progression \(a_1, a_2, a_3, \ldots\) with \(a_1=\frac{1}{8}\) and \(a_2 \neq a_1\), is the arithmetic mean of the next two terms and \(S_n=a_1+a_2+\ldots+a_n\), then \(\mathrm{S}_{20}-\mathrm{S}_{18}\) is equal toJEE Mains 2024 Hard
- A small bob of mass 100 mg and charge \(+10 \mu \mathrm{C}\) is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density ' \(\sigma\) ' as shown in figure. If string subtends an angle of \(45^{\circ}\) with the sheet at equilibrium the charge density of sheet will be :
(Given, \(\varepsilon_0=8.85 \times 10^{-12} \frac{\mathrm{~F}}{\mathrm{~m}}\) and acceleration due to gravity, \(g=10 \mathrm{~m} / \mathrm{s}^2\))
JEE Mains 2025 Medium