Physics and Engineering of Radiation Detection

3.5. Proportional Counters 187

For argonDα=1. 81 × 10 −^17 cm^2 /V(see Table 3.3.1) and its molecular number

density can be calculated from

Nm=

NAρ

A

,

whereNAis the Avogadro’s number,ρis the weight density, andAis the

atomic mass. Hence for argon we have

Nm =

(6. 022 × 1023 )(1. 784 × 10 −^3 )

18

=5. 97 × 1019 atoms/cm^3.

Substituting all these values in equation 3.5.8 we get

M =exp

[

2

(

(1. 81 × 10 −^17 )(5. 97 × 1019 )(V 0 )(10−^3 )

ln(3/ 10 −^3 )

) 1 / 2 (√

V 0

500

− 1

)]

=exp

[

0. 73

√

V 0

(√

V 0

500

− 1

)]

.

The required plot of this equation is shown in Fig.3.5.3.

Applied Voltage (V)

500 600 700 800 900 1000

M

1

10

102

103

104

Figure 3.5.3: Variation of multiplication

factor with applied voltage for an argon

filled proportional counter.