Substance A has atomic mass number 16 and half-life of 1 day. Another substance π΅ has atomic mass number 32 and half life of $\frac1{ 2}$ day. If both π΄ and π΅ 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.
- $3.38Γ10^{24 }$
- $ 1.69Γ10^{24 } $
- $ 6.76Γ10^{24 } $
- $ 6.76Γ10^{23} $
The Correct Option is A
Solution and Explanation
\[ (N_0)_A = \frac{320}{16} = 20 \, \text{moles} \] \[ N_A = (N_0)_A \left(\frac{1}{2}\right)^2 = 20 \times \frac{1}{4} = 5 \, \text{moles} \] For substance B:
\[ (N_0)_B = \frac{320}{32} = 10 \, \text{moles} \] \[ N_B = (N_0)_B \left(\frac{1}{2}\right)^4 = 10 \times \frac{1}{16} = 0.625 \, \text{moles} \] Total moles = \(5 + 0.625 = 5.625\). The total number of atoms: \[ 5.625 \times 6.023 \times 10^{23} = 3.38 \times 10^{24} \]
Top Questions on Nuclear physics
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): The density of the copper ($^{64}Cu$) nucleus is greater than that of the carbon ($^{12}C$) nucleus.
Reason (R): The nucleus of mass number A has a radius proportional to $A^{1/3}$.
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Match the LIST-I with LIST-II
\[ \begin{array}{|l|l|} \hline \text{LIST-I} & \text{LIST-II} \\ \hline A. \ ^{236}_{92} U \rightarrow ^{94}_{38} Sr + ^{140}_{54} Xe + 2n & \text{I. Chemical Reaction} \\ \hline B. \ 2H_2 + O_2 \rightarrow 2H_2O & \text{II. Fusion with +ve Q value} \\ \hline C. \ ^3_1 H + ^2_1 H \rightarrow ^4_2 He + n & \text{III. Fission} \\ \hline D. \ ^1_1 H + ^3_1 H \rightarrow ^4_2 H + \gamma & \text{IV. Fusion with -ve Q value} \\ \hline \end{array} \]
Choose the correct answer from the options given below:
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Concepts Used:
Nuclear Physics
Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the atom as a whole, including its electrons
Radius of Nucleus
βRβ represents the radius of the nucleus. R = RoA1/3
Where,
- Ro is the proportionality constant
- A is the mass number of the element
Total Number of Protons and Neutrons in a Nucleus
The mass number (A), also known as the nucleon number, is the total number of neutrons and protons in a nucleus.
A = Z + N
Where, N is the neutron number, A is the mass number, Z is the proton number
Mass Defect
Mass defect is the difference between the sum of masses of the nucleons (neutrons + protons) constituting a nucleus and the rest mass of the nucleus and is given as:
Ξm = Zmp + (A - Z) mn - M
Where Z = atomic number, A = mass number, mp = mass of 1 proton, mn = mass of 1 neutron and M = mass of nucleus.