Askiitians Tutor Team
Last Activity: 12 Days ago
To determine the current produced in the ionization chamber by the alpha particles emitted from the uranium sample, we need to follow a series of logical steps. Let's break this down together.
Understanding the Basics
Alpha particles are a type of ionizing radiation consisting of two protons and two neutrons. When they interact with the air or any gas in the ionization chamber, they can ionize the gas molecules, creating ion pairs. Each ion pair consists of a positive ion and a free electron.
Key Values and Constants
- Energy of each alpha particle: 4.2 MeV
- Rate of alpha particles entering the chamber: 15 particles/second
- Energy required to create one ion pair: 30 eV
- Charge of an electron (e): 1.6 × 10-19 C
Calculating Ion Pairs Created
First, we need to find out how many ion pairs are produced per second from the alpha particles. Since each alpha particle has an energy of 4.2 MeV, we can convert this energy into electron volts (eV) for easier calculations:
1 MeV = 1,000,000 eV, so:
4.2 MeV = 4.2 × 106 eV
Now, we can calculate how many ion pairs can be created from the energy of one alpha particle:
Number of ion pairs produced by one alpha particle:
Number of ion pairs = Energy of alpha particle / Energy required for one ion pair
Number of ion pairs = (4.2 × 106 eV) / (30 eV) = 140,000 ion pairs
Calculating Total Ion Pairs per Second
Since we have 15 alpha particles entering the chamber every second, we can find the total number of ion pairs produced per second:
Total ion pairs per second = Number of ion pairs per alpha particle × Rate of alpha particles
Total ion pairs per second = 140,000 ion pairs × 15 particles/second = 2,100,000 ion pairs/second
Finding the Current
Now that we know how many ion pairs are produced, we can calculate the current. Each ion pair produces one electron, and the charge of one electron is 1.6 × 10-19 C. The current (I) can be calculated using the formula:
I = Charge per second
Charge per second = Number of ion pairs per second × Charge of one electron
Charge per second = 2,100,000 ion pairs/second × 1.6 × 10-19 C
Calculating this gives:
Charge per second = 2,100,000 × 1.6 × 10-19 C = 3.36 × 10-13 C/second
Since current is measured in Amperes (A), and 1 A = 1 C/s, we find:
I = 3.36 × 10-13 A
Final Result
The current produced in the ionization chamber due to the alpha particles emitted from the uranium sample is approximately 3.36 × 10-13 A.