Question:
The probability of survival of a radioactive nucleus for one mean life is
The probability of survival of a radioactive nucleus for one mean life is
Updated On: Jun 27, 2023
- $\frac{1}{e}$
- $1-\frac{1}{e}$
- $\frac{1n 2}{e}$
- $1-\frac{1n 2}{e}$
Hide Solution
Verified By Collegedunia
The Correct Option is A
Approach Solution - 1
Probability of survival for any nucleus at time $t$ is
$P = \frac{N}{N_0} = \frac{N_0 e^{- \lambda t}}{N_0} = e^{-\lambda t}$
So, in one mean life, required probability
is $e^{- \lambda = \frac{1}{\lambda}} = \frac{1}{e}$
Was this answer helpful?
0
0
Hide Solution
Verified By Collegedunia
Approach Solution -2
The probability of survival of a radioactive nucleus for one mean life is
Was this answer helpful?
0
0
Top Questions on Nuclei
- If the radius of the first Bohr orbit is \( r \), then the radius of the second Bohr orbit will be
- 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 \( = 3 \times 10^8 \, \text{m/s} \))
- The half-lives of two radioactive materials A and B are respectively \( T \) and \( 2T \). If the ratio of the initial masses of the materials A and B is 8:1, then the time after which the ratio of the masses of the materials A and B becomes 4:1 is:
- 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 \( c^2 = 931 \, \text{MeV/u} \). - In a nuclear reactor of efficiency 25%, the number of fissions taking place per second is \( 5 \times 10^{13} \). If 200 MeV energy is released per fission, then the output power of the reactor is:
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