JEE Mains · Physics · STD 12 - Nuclei
- JEE Mains 2023
- Medium
- MCQ
Substance \(A\) has atomic mass number \(16\) and half life of \(1\) day. Another substance \(B\) has atomic mass number \(32\) and half life of \(\frac{1}{2}\) day. If both \(A\) and \(B\) simultaneously start undergo radio activity at the same time with initial mass \(320\,g\) each, how many total atoms of \(A\) and \(B\) combined would be left after \(2\) days \(.........\times 10^{24}\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(3.38\)
Step-by-step Solution
Detailed explanation
\(\left( N _0\right) A =\frac{320}{16}=20 \text { moles }\)
\(\left( N _0\right) B =\frac{320}{32}=10 \text { moles }\)
\(N _{ A }=\frac{\left( N _0\right)_{ A }}{(2)^{2 / 1}}=\frac{20}{4}=5\)
\(N _{ B }=\frac{\left( N _0\right)_{ B }}{(2)^{2 / 5}}=\frac{10}{2^4}=0.625\)
Total \(N =5.625\)
No. of atoms \(=5.625 \times 6.023 \times 10^{23}\)
More questions from Physics
- Consider a spherical shell of radius \(R\) at temperature \(T\). The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume\(E=\) \(\frac{U}{V} \propto {T^4}\) and pressure \(P = \frac{1}{3}\left( {\frac{U}{V}} \right)\) If the shell now undergoes an adiabatic expansion the relation between \(T\) and \(R\) isJEE Mains 2015 Hard
- A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius \(\mathrm{R} / 2\) is removed from the original disc as shown in the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above.
JEE Mains 2025 Medium - In a radioactive decay chain, the initial nucleus is \({}_{90}^{232}Th\). At the end there are \(6\,\,\alpha -\) particles and \(4\,\,\beta -\) particles with are emitted. If the end nucleus is \({}_Z^AX\,,\,A\) and \(Z\) are given byJEE Mains 2019 Medium
- In an expression a \(\times 10^{\mathrm{b}}\) _______.JEE Mains 2024 Easy
- A constant magnetic field of \(1 \,{T}\) is applied in the \({x}\,>\,0\) region. A metallic circular ring of radius \(1 \,{m}\) is moving with a constant velocity of \(1 \,{m} / {s}\) along the \(x\)-axis. At \(t=0\) \(s,\) the centre of \(O\) of the ring is at \({x}=-1 \,{m}\). What will be the value of the induced \(emf\) in the ring at \(t=1\, s\) ? (Assume the velocity of the ring does not change.) (In \({V}\))
JEE Mains 2021 Hard - A cylinder with adiabatic walls is closed at both ends and is divided into two compartments by a frictionless adiabatic piston. Ideal gas is filled in both (left and right) the compartments at same \(P, V, T\). Heating is started from left side until pressure changes to \(\dfrac{27P}{8}\). If initial volume of each compartment was \(9\) litres then the final volume in right-hand side compartment is __________ litres. (for this ideal gas \(C_P/C_V = 1.5\))JEE Mains 2026 Hard
More PYQs from JEE Mains
- Force acts for \(20\,s\) on a body of mass \(20\,kg\), starting from rest, after which the force ceases and then body describes \(50\,m\) in the next \(10\,s\). The value of force will be \(..........\,N\)JEE Mains 2023 Medium
- A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength \(980\,\mathop A\limits^o \). The radius of the atom in the excited state, in terms of Bohr radius \(a_0,\) will be \((hc\,=\,12500\,eV-\mathop A\limits^o)\)JEE Mains 2019 Hard
- An \(npn\) transistor operates as a common emitter amplifier with a power gain of \(10^{6} .\) The input circuit resistance is \(100\, \Omega\) and the output load resistance is \(10\, K \Omega\). The common emitter current gain ' \(\beta\) ' will be............. (Round off to the Nearest Integer)JEE Mains 2021 Medium