Question:
The half-life of radioactive radon is 3.8 days. The time at the end of which \(\frac{1}{20}th\) of the Radon sample will remain undecayed is (given log10e=0.4343)
The half-life of radioactive radon is 3.8 days. The time at the end of which \(\frac{1}{20}th\) of the Radon sample will remain undecayed is (given log10e=0.4343)
Updated On: Apr 19, 2024
- 3.8 days
- 16.5 days
- 33 days
- 76 days
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is B)
t\(_\frac{1}{2}\) =3.8 day
∴ λ = \(\frac{0.693}{t_\frac{1}{2}}\)=\( \frac{0.693}{3.8}\)= 0.182
If the initial number of atoms is a=A0 then after time t the number of atoms is \(\frac{a}{20}\) = a
\(t=\frac{2.303}{\lambda}log\frac{A_0}{A}=\frac{2.303}{0.182}log\frac{a}{a/20}\)
\(=\frac{2.303}{0.182}log 20 = 16.46\)
t\(_\frac{1}{2}\) =3.8 day
∴ λ = \(\frac{0.693}{t_\frac{1}{2}}\)=\( \frac{0.693}{3.8}\)= 0.182
If the initial number of atoms is a=A0 then after time t the number of atoms is \(\frac{a}{20}\) = a
\(t=\frac{2.303}{\lambda}log\frac{A_0}{A}=\frac{2.303}{0.182}log\frac{a}{a/20}\)
\(=\frac{2.303}{0.182}log 20 = 16.46\)
Was this answer helpful?
6
0
Top Questions on Nuclei
- The disintegration energy \( Q \) for the nuclear fission of \( ^{235}\text{U} \to ^{140}\text{Ce} + ^{94}\text{Zr} + n \) is _____ MeV.
Given atomic masses:
\[^{235}\text{U} = 235.0439 \, u, \quad ^{140}\text{Ce} = 139.9054 \, u, \quad ^{94}\text{Zr} = 93.9063 \, u, \quad n = 1.0086 \, u\]Value of \( c^2 = 931 \, \text{MeV/u} \). - The mass defect in a particular reaction is \( 0.4 \, \text{g} \). The amount of energy liberated is \( n \times 10^7 \, \text{kWh} \), where \( n = \) _____. (speed of light \( = 3 \times 10^8 \, \text{m/s} \))
- A nucleus has mass number \(A_1\) and volume \(V_1\). Another nucleus has mass number \(A_2\) and volume \(V_2\). If the relation between mass numbers is \(A_2 = 4A_1\), then \(\frac{V_2}{V_1} =\) _______.
- The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is:
- A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration they will move
View More Questions
Questions Asked in VITEEE exam
- Two identical blocks A and B, each of mass 'm' resting on a smooth floor are connected by a light spring of natural length L and spring constant K, with the spring at its natural length. A third identical block 'C' (mass m) moving with a speed v along the line joining A and B collides with A. the maximum compression in the spring is
- VITEEE - 2023
- work, energy and power
- Which element has more electron gain enthalpy among chalcogen group?
- VITEEE - 2022
- sulphur
- Coin is tossed till heads is obtained what is expectation of no. of coin tosses
- VITEEE - 2022
- Random Variables
- Which of the following shows Frenkel's defect?
- VITEEE - 2022
- The solid state
- Which of the following lanthanides are in tv screen.
- VITEEE - 2022
- d -and f -Block Elements
View More Questions
Concepts Used:
Nuclei
In the year 1911, Rutherford discovered the atomic nucleus along with his associates. It is already known that every atom is manufactured of positive charge and mass in the form of a nucleus that is concentrated at the center of the atom. More than 99.9% of the mass of an atom is located in the nucleus. Additionally, the size of the atom is of the order of 10-10 m and that of the nucleus is of the order of 10-15 m.
Read More: Nuclei
Following are the terms related to nucleus:
- Atomic Number
- Mass Number
- Nuclear Size
- Nuclear Density
- Atomic Mass Unit