JEE Mains · Physics · STD 12 - 13. Nuclei
A sample of radioactive material \(A\), that has an activity of \(10\, mCi\, (1\, Ci = 3.7 \times 10^{10}\, decays/s)\), has twice the number of nuclei as another sample of different radioactive material \(B\) which has an activity of \(20\, mCi\). The correct choices for half-lives of \(A\) and \(B\) would then be respectively
- A \(5\) days and \(10\) days
- B \(10\) days and \(40\) days
- C \(20\) days and \(5\) days
- D \(20\) days and \(10\) days
Answer & Solution
Correct Answer
(B) \(10\) days and \(40\) days
Step-by-step Solution
Detailed explanation
Activity \(=\lambda\) (number of atoms) \(10=\lambda_{A} N_{A}\) ..... \((1)\) \(20=\lambda_{B} N_{B}\) ..... \((2)\) \(N_{A}=2 N_{B}\) ..... \((3)\) Solving we get, \(\frac{\lambda_{A}}{\lambda_{B}}=\frac{1}{4}\)
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
- Let \(\left| {{{\vec A}_1}} \right| = 3,\,\left| {\vec A_2} \right| = 5\), and \(\left| {{{\vec A}_1} + {{\vec A}_2}} \right| = 5\). The value of \(\left( {2{{\vec A}_1} + 3{{\vec A}_2}} \right)\cdot \left( {3{{\vec A}_1} - 2{{\vec A}_2}} \right)\) isJEE Mains 2019 Hard
- In meter bridge experiment for measuring unknown resistance ' \(S\) ', the null point is obtained at a distance \(30 cm\) from the left side as shown at point \(D\). If \(R\) is \(5.6 k \Omega\), then the value of unknown resistance ' \(S\) ' will be \(\Omega .\)
JEE Mains 2022 Medium - Two particles \({A}\) and \({B}\) having charges \(20\, \mu {C}\) and \(-5\, \mu {C}\) respectively are held fixed with a separation of \(5\, {cm}\). At what position a third charged particle should be placed so that it does not experience a net electric force?
JEE Mains 2021 Medium - The temperature of equal masses of three different liquids \({x}, {y}\) and \({z}\) are \(10^{\circ} {C}, 20^{\circ} {C}\) and \(30^{\circ} {C}\) respectively. The temperature of mixture when \({x}\) is mixed with \({y}\) is \(16^{\circ} {C}\) and that when \({y}\) is mixed with \(z\) is \(26^{\circ} {C}\). The temperature of mixture when \(x\) and \(z\) are mixed will be ...... \(^{\circ} {C}\)JEE Mains 2021 Hard
- A thermally insulated vessel contains an ideal gas of molecular mass \(M\) and ratio of specific heats \(1.4\). Vessel is moving with speed \(v\) and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by ... ( \(R =\) universal gas constant )JEE Mains 2022 Medium
- The \(rms\) speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are \({V}_{{H}}, {V}_{0}\) and \({V}_{{C}}\) respectively thenJEE Mains 2021 Medium
More PYQs from JEE Mains
- Given below are two statements: Statement \(I :\) A second's pendulum has a time period of \(1\) second. Statement \(II :\) It takes precisely one second to move between the two extreme positions. In the light of the above statements, choose the correct answer from the options given below:JEE Mains 2021 Medium
- Let \(P\) be the point on the parabola \({y^2} = 8x\) which is at a minimun distance from the centre \(C\) of the circle \({x^2} + {\left( {y + 6} \right)^2} = 1\) . Then the equation of the circle , passing through \(C\) and having its centre at \(P \) is :JEE Mains 2016 Hard
- An ac source is connected in given series \(LCR\) circuit. The rms potential difference across the capacitor of \(20 \mu \mathrm{F}\) is _______\(v\). [\(\mathrm{V}=50 \sqrt{2} \sin 100 \mathrm{t}\) volt]
JEE Mains 2024 Hard - Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure
JEE Mains 2019 Hard - Let the relation R on the set \(M=\{1,2,3,.......16\}\) be given by \(R=\{(x,y):4y=5x-3,x,y\in M\}\). Then the minimum number of elements required to be added in R, in order to make the relation symmetric, is equal toJEE Mains 2026 Hard
- Two plane mirrors are inclined to each other such that a ray of light incident to the first mirror \((M_1)\) and parallel to the second mirror \((M_2)\) is finally reflected from the second mirror \((M_2)\) parallel to the first mirror \((M_1).\) The angle between the two mirrors will be......\(^o\)JEE Mains 2019 Medium