JEE Mains · Physics · STD 12 - 13. Nuclei
A piece of bone of an animal from a ruin is found to have \(^{14}C\) activity of \(12\) disintegrations per minute per gm of its carbon content. The \(^{14}C\) activity of a living animal is \(16\) disintegrations per minute per gm. How long ago nearly did the animal die? ............\(years\) (Given halflife of \(^{14}C\) is \(t_{1/2} = 5760\,years\) )
- A \(1672\)
- B \(2391\)
- C \(3291\)
- D \(4453\)
Answer & Solution
Correct Answer
(B) \(2391\)
Step-by-step Solution
Detailed explanation
Given, for \(^{14} \mathrm{C}\) \(A_{0}=16\) dis \(\min ^{-1} g^{-1}\) \(A=12\) dis \(\min ^{-1} g^{-1}\) \(\mathrm{t}_{1 / 2}=5760\) years Now, \(\lambda = \frac{{0.693}}{{{t_{1/2}}}}\) \(\lambda=\frac{0.693}{5760}\) per year Then, from,…
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 heavy iron bar of weight \(12 \mathrm{~kg}\) is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle \(60^{\circ}\) with the horizontal, the weight experienced by the man is :JEE Mains 2024 Hard
- de-Broglie wavelength of an electron accelerated by a voltage of \(50\,\,V\) is close to ............. \(\mathop {\rm{A}}\limits^o \) \((\left| e \right| = 1.6 \times {10^{ - 19}}\,\,C,\,\,{m_e} = 9.1 \times {10^{ - 31}}\,kg,\,\,h = 6.6 \times {10^{ - 34}}\,\,Js)\)JEE Mains 2015 Medium
- A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to \(\operatorname{arc} \mathrm{AB}\) to ' O ' is ' E ' is magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?
JEE Mains 2025 Hard - From a sphere of mass \(M\) and radius \(R\), a smaller sphere of radius \(\frac{R}{2}\) is carved out such that the cavity made in the original sphere is between its centre and the periphery (See figure) . For the configuration in the figure where the distance between the centre of the original sphere and the removed sphere is \(3R\), the gravitational force between the two sphere is
JEE Mains 2014 Hard - A student determined Young's Modulus of elasticity using the formula \(Y=\frac{M g L^{3}}{4 b d^{3} \delta} .\) The value of \(g\) is taken to be \(9.8 \,{m} / {s}^{2}\), without any significant error, his observation are as following.
Then the fractional error in the measurement of \({Y}\) isPhysical Quantity Least count of the Equipment used for measurement Observed value Mass \(({M})\) \(1\; {g}\) \(2\; {kg}\) Length of bar \((L)\) \(1\; {mm}\) \(1 \;{m}\) Breadth of bar \((b)\) \(0.1\; {mm}\) \(4\; {cm}\) Thickness of bar \((d)\) \(0.01\; {mm}\) \(0.4 \;{cm}\) Depression \((\delta)\) \(0.01\; {mm}\) \(5 \;{mm}\) JEE Mains 2021 Hard - A common emitter amplifier circuit, built using an \(npn\) transistor, is shown in the figure. Its \(dc\) current gain is \(250\), \(R_C = 1\,k\, \Omega \) and \(V_{CC} = 10\,V\). What is the minimum base current for \(V_{CE}\) to reach saturation?.........\(\mu A\)
JEE Mains 2019 Medium
More PYQs from JEE Mains
- The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be \(45^{\circ} .\) After walking a distance of \(80\) meters towards the top, up a slope inclined at an angle of \(30^{\circ}\) to the horizontal plane, the angle of elevation of the top of the hill becomes \(75^{\circ} .\) Then the height of the hill (in meters) isJEE Mains 2020 Hard
- A gas molecule of mass \(M\) at the surface of the Earth has kinetic energy equivalent to \(0\,^oC\). If it were to go up straight without colliding with any other molecules, how high it would rise? Assume that the height attained is much less than radius of the earth. (\(k_B\) is Boltzmann constant)JEE Mains 2014 Medium
- An object of mass \(0.2 \mathrm{~kg}\) executes simple harmonic motion along \(\mathrm{x}\) axis with frequency of \(\left(\frac{25}{\pi}\right) \mathrm{Hz}\). At the position \(\mathrm{x}=0.04 \mathrm{~m}\) the object has kinetic energy \(0.5 \mathrm{~J}\) and potential energy \(0.4 \mathrm{~J}\) The amplitude of oscillation is _______ cm.JEE Mains 2024 Hard
- \(\text { If } \int \frac{1}{\sqrt[5]{(x-1)^4(x+3)^6}} d x=A\left(\frac{\alpha x-1}{\beta x+3}\right)^B+C,\) where \(\mathrm{C}\) is the constant of integration, then the value of \(\alpha+\beta+20 \mathrm{AB}\) is ...........JEE Mains 2024 Hard
- A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant \(\varepsilon_1\) and \(\varepsilon_2\), as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are \(C_1\) and \(C_2\) respectively, then \(\frac{C_1}{C_2}\) is :
JEE Mains 2025 Hard - In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of \(7.5 \times 10^{-12}\, m\), the minimum electron energy required is close to .............. \(keV\)JEE Mains 2019 Medium