Efficiency of a GM Counter is 90% and Maximum Counting Rate of its is 6000 per minute. Calculate Paralysis Time of Counter in second.
SOLUTION : Geiger-Muller (GM) counters are essential instruments in radiation detection, widely used to measure ionizing radiation levels. They operate on the principle of detecting individual ionizing events and are particularly sensitive to low levels of radiation. However, these counters experience a phenomenon known as "paralysis" when exposed to high radiation rates.
Efficiency and Counting Rate:
The efficiency of a GM counter refers to its ability to detect and register radiation events accurately. It is expressed as a percentage and represents the ratio of the number of recorded events to the total number of events.
In your case, the efficiency (\( \eta \)) is given as 90%, or 0.9.
The maximum counting rate (\( R \)) is the highest rate at which the counter can register events. It is typically measured in counts per unit time, such as counts per minute (CPM).
In this scenario, the maximum counting rate is \( R = 6000 \) counts per minute.
Paralysis Time:
Paralysis in a GM counter occurs when the radiation rate is so high that the counter cannot process each event before the next one occurs. During paralysis, the counter effectively stops registering events.
The relationship between efficiency, counting rate, and paralysis time (\( \tau \)) is described by the equation:
\[ R = \frac{\eta}{\tau} \]
Solving for paralysis time:
\[ \tau = \frac{\eta}{R} \]
Calculation:
Given that \( \eta = 0.9 \) and \( R = 6000 \) counts per minute, let's calculate the paralysis time (\( \tau \)) in seconds.
\[ \tau = \frac{0.9}{6000/60} \]
To calculate the paralysis time (\( \tau \)), we use the formula:
\[ \tau = \frac{\eta}{R} \]
Given:
- Efficiency (\( \eta \)) = 90% or 0.9
- Maximum counting rate (\( R \)) = 6000 counts per minute
Let's convert the maximum counting rate to counts per second (\( R_{\text{sec}} \)) by dividing it by 60 (since there are 60 seconds in a minute):
\[ R_{\text{sec}} = \frac{6000}{60} = 100 \, \text{counts per second} \]
Now, substitute these values into the formula:
\[ \tau = \frac{0.9}{100} \]
Calculating this:
\[ \tau = 0.009 \, \text{seconds} \]
Therefore, the paralysis time (\( \tau \)) of the GM counter under these conditions is approximately 0.009 seconds. This means that in high radiation environments, the counter may experience paralysis for a very short duration before it can resume accurate counting.
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