JEE Mains · Physics · STD 12 - 13. Nuclei
A radioactive nucleus can decay by two different processes. Half-life for the first process is \(3.0\, hours\) while it is \(4.5\, hours\) for the second process. The effective half- life of the nucleus will be \(.........\,hours.\)
- A \(3.75\)
- B \(0.56\)
- C \(0.26\)
- D \(1.80\)
Answer & Solution
Correct Answer
(D) \(1.80\)
Step-by-step Solution
Detailed explanation
\(\lambda_{\text {eq }}=\lambda_{1}+\lambda_{2}\) \(\frac{\ln 2}{\left( t _{1 / 2}\right)_{ eq }}=\frac{\ln 2}{\left( t _{1 / 2}\right)_{1}}+\frac{\ln 2}{\left( t _{1 / 2}\right)_{2}}\)…
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
- Three rods of Copper, Brass and Steel are welded together to form a \(Y\) shaped structure. Area of cross - section of each rod \(= 4\ cm^2\) . End of copper rod is maintained at \(100^o C \) where as ends ofbrass and steel are kept at \(0^o C\). Lengths of the copper, brass and steel rods are \(46, 13\) and \(12\ cms\) respectively. The rods are thermally insulated from surroundings excepts at ends. Thermal conductivities of copper, brass and steel are \(0.92, 0.26\) and \(0.12\ CGS\) units respectively. Rate ofheat flow through copper rod is ....... \(cal\, s^{-1}\)JEE Mains 2014 Hard
- Water boils in an electric kettle in \(20\) minutes after being switched on. Using the same main supply, the length of the heating element should be _______ to _______ times of its initial length if the water is to be boiled in \(15\) minutes.JEE Mains 2024 Hard
- A plane progressive wave is given by \(y=2 \cos 2 \pi(330 t-x) m\). The frequency of the wave is _______.JEE Mains 2024 Hard
- A short bar magnet placed with its axis at \(30^{\circ}\) with an external field of 800 Gauss, experiences a torque of \(0.016 N . m\). The work done in moving it from most stable to most unstable position is \(\alpha \times 10^{-3} J\). The value of \(\alpha\) is _________ .JEE Mains 2026 Medium
- An electron is moving along \(+x\) direction with a velocity of \(6 \times 10^{6}\, ms ^{-1}\). It enters a region of uniform electric field of \(300 \,V / cm\) pointing along \(+ y\) direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the \(x\) direction will beJEE Mains 2020 Hard
- In the reported figure, there is a cyclic process \(ABCDA\) on a sample of \(1\, {mol}\) of a diatomic gas. The temperature of the gas during the process \({A} \rightarrow {B}\) and \({C} \rightarrow {D}\) are \({T}_{1}\) and \({T}_{2}\left({T}_{1}\,>\,{T}_{2}\right)\) respectively. Choose the correct option out of the following for work done if processes \(B C\) and \(D A\) are adiabatic.
JEE Mains 2021 Medium
More PYQs from JEE Mains
- The distance of the point \((-1,2,-2)\) from the line of intersection of the planes \(2 \mathrm{x}+3 \mathrm{y}+2 \mathrm{z}=0\) and \(x-2 y+z=0\) is :JEE Mains 2021 Medium
- Let \(f\) be any function continuous on \([\mathrm{a}, \mathrm{b}]\) and twice differentiable on \((a, b) .\) If for all \(x \in(a, b)\) \(f^{\prime}(\mathrm{x})>0\) and \(f^{\prime \prime}(\mathrm{x})<0,\) then for any \(\mathrm{c} \in(\mathrm{a}, \mathrm{b})\) \(\frac{f(\mathrm{c})-f(\mathrm{a})}{f(\mathrm{b})-f(\mathrm{c})}\) is greater thanJEE Mains 2020 Hard
- The fifth harmonic of a closed organ pipe is found to be in unison with the first harmonic of an open pipe. The ratio of lengths of closed pipe to that of the open pipe is \(5 / x\). The value of \(x\) is _________ .JEE Mains 2026 Hard
- The transfer characteristic curve of a transistor, having input and output resistance \(100\,\Omega \) and \(100\,k\Omega \) respectively, is shown in the figure. The Voltage and Power gain, are respectively
JEE Mains 2019 Hard - Let \(\lambda^{*}\) be the largest value of \(\lambda\) for which the function \(f _{\lambda}( x )=4 \lambda x ^{3}-36 \lambda x ^{2}+36 x +48\) is increasing for all \(x \in R\). Then \(f _{\lambda} *(1)+ f _{\lambda} *(-1)\) is equal toJEE Mains 2022 Hard
- \(\lim _{x \rightarrow \frac{\pi}{2}}\left(\frac{1}{\left(x-\frac{\pi}{2}\right)^2} \int_{x^3}^{\left(\frac{\pi}{2}\right)^3} \cos \left(\frac{1}{t^3}\right) d t\right)\) is equal toJEE Mains 2024 Hard