5.12 Dead Time of Geiger–Müller Counter
89
multiplying the numerator and the denominator of Eq. (5.4) by (1 + m 1 τ ) and
since numerically m 12 τ
2 is much smaller than unity (since τ is usually of the
order of (100 − 300 ms), one gets from Eq. (5.4)
n 1 =
m 1
(1 − m
2
1 τ 2 )
≈ m 1 (1 + m 1 τ ) per second
(5.8)
In order to evaluate this equation, we have to take the help of activities measured
for both samples (i.e., m 12 ). n b Eq. (5.7) can be assumed to be equal to m b , because
m b × τ would be a very small number and hence can be neglected. Moreover,
(n 1 + n 2 ) should be equal to (n 12 + n b ). Here, n b is added because L.H.S. is
counted twice (which would include the background twice). By substituting the
values of n 1 , n 12 and n b from the previous equations, we get
m 1 (1 + m 1 τ ) + m 2 (1 + m 2 × τ ) = m 12 (1 + m 12 × τ ) + m b
or
τ =
m 12 + m b − m 1 − m 2
m
2
1 + m
2
2 − m
2
12
(5.9)
In this manner, the dead time of the counter (τ ) can be determined. The main
problem with this method is in making two sources having geometrically identical
conditions with almost same activity and making sure that m
2
1 τ
2 , m
2
2 τ
2 , and m
2
12 τ
2
are less than one. This derivation also clarifies how tedious it would be if we have
to determine the dead time of the counter whenever we have to carry out the
counting procedure.
2. Electronic Quenching method: The value of dead time determined by the above
method is valid for the counter for which it was measured, because each counter
has its own dead time depending on the geometry of construction and composition
of gas filled in the counter. Moreover, dead time is not always constant; as the
counter becomes older, this value changes slightly. Therefore, one will have to
determine the dead time of the counter, prior to use. In radiochemical work, it will
become very difficult to determine the dead time of every G.M. counter each time,
before it is used for counting purpose. However, it is possible to have a quencher
unit, which allows the anode to rest for a period, e.g., 400 ms or 600 ms, which
is greater than the normal dead time of the counter. This means that after every
count recorded, the counter will remain dead for a set of known period.
The set period is always kept greater than the natural dead time of the counter.
The quencher unit after recording each radiation lowers the anode potential much
below its normal operating voltage so that the counter cannot respond to the
incoming radiation. After a lapse of say 400 ms, or any such time set by the
quencher unit, the anode potential is automatically brought back to its original
potential. Thus, counter always receives a new radiation at its operating anode
potential. Observed count is then corrected according to the artificial dead time
89
multiplying the numerator and the denominator of Eq. (5.4) by (1 + m 1 τ ) and
since numerically m 12 τ
2 is much smaller than unity (since τ is usually of the
order of (100 − 300 ms), one gets from Eq. (5.4)
n 1 =
m 1
(1 − m
2
1 τ 2 )
≈ m 1 (1 + m 1 τ ) per second
(5.8)
In order to evaluate this equation, we have to take the help of activities measured
for both samples (i.e., m 12 ). n b Eq. (5.7) can be assumed to be equal to m b , because
m b × τ would be a very small number and hence can be neglected. Moreover,
(n 1 + n 2 ) should be equal to (n 12 + n b ). Here, n b is added because L.H.S. is
counted twice (which would include the background twice). By substituting the
values of n 1 , n 12 and n b from the previous equations, we get
m 1 (1 + m 1 τ ) + m 2 (1 + m 2 × τ ) = m 12 (1 + m 12 × τ ) + m b
or
τ =
m 12 + m b − m 1 − m 2
m
2
1 + m
2
2 − m
2
12
(5.9)
In this manner, the dead time of the counter (τ ) can be determined. The main
problem with this method is in making two sources having geometrically identical
conditions with almost same activity and making sure that m
2
1 τ
2 , m
2
2 τ
2 , and m
2
12 τ
2
are less than one. This derivation also clarifies how tedious it would be if we have
to determine the dead time of the counter whenever we have to carry out the
counting procedure.
2. Electronic Quenching method: The value of dead time determined by the above
method is valid for the counter for which it was measured, because each counter
has its own dead time depending on the geometry of construction and composition
of gas filled in the counter. Moreover, dead time is not always constant; as the
counter becomes older, this value changes slightly. Therefore, one will have to
determine the dead time of the counter, prior to use. In radiochemical work, it will
become very difficult to determine the dead time of every G.M. counter each time,
before it is used for counting purpose. However, it is possible to have a quencher
unit, which allows the anode to rest for a period, e.g., 400 ms or 600 ms, which
is greater than the normal dead time of the counter. This means that after every
count recorded, the counter will remain dead for a set of known period.
The set period is always kept greater than the natural dead time of the counter.
The quencher unit after recording each radiation lowers the anode potential much
below its normal operating voltage so that the counter cannot respond to the
incoming radiation. After a lapse of say 400 ms, or any such time set by the
quencher unit, the anode potential is automatically brought back to its original
potential. Thus, counter always receives a new radiation at its operating anode
potential. Observed count is then corrected according to the artificial dead time