A sample contains \(10^{–2}\) kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is \(\frac {x}{100}\). The value of \(x\) is ______.
Correct Answer: 25
Solution and Explanation
\(N_1 = \frac {(\frac {10^{-2}}{1})}{24}\)
\(N_2 = \frac {(\frac {10^{-2})}{2}}{2^2}\)
\(⇒ \frac {N_1}{N_2}=\frac 12\)
∴ Mass ratio of A and B,
\(\frac {m_1}{m_2}= \frac {N_1}{N_2} \times \frac {M_1}{M_2} \)
\(= \frac 12 \times (\frac 12)\)
\(= \frac 14\)
\(=\frac {25}{100}\)
Given that, the ratio of the amounts of A and B after 16 s is \(\frac {x}{100}\).
On comparing, \(x = 25\)
So, the answer is \(25\).
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Concepts Used:
Atomic Physics
Atomic physics is the study of the behavior and properties of atoms, which are the fundamental building blocks of matter. Atoms consist of a nucleus, which is made up of positively charged protons and neutral neutrons, surrounded by a cloud of negatively charged electrons. The behavior of these particles is governed by the laws of quantum mechanics, which describe the behavior of particles at the atomic and subatomic level.
One of the most important concepts in atomic physics is the electronic structure of atoms, which refers to the arrangement of electrons in the atom's energy levels or orbitals. These energy levels determine the chemical and physical properties of an atom, including its reactivity and spectral characteristics.
Another important area of atomic physics is the study of atomic spectra, which are the unique patterns of electromagnetic radiation emitted or absorbed by atoms. These spectra can be used to identify the elements present in a sample and to determine their electronic structure.
Atomic physics also encompasses the study of atomic collisions, in which two or more atoms interact and exchange energy. These collisions can lead to a variety of phenomena, including chemical reactions, excitation and ionization of atoms, and the creation of new particles.
Overall, atomic physics is a fascinating field of study that has applications in many areas of science and technology, including materials science, chemistry, and electronics.