Physics and Radiobiology of Nuclear Medicine

Standard Deviation of Count Rates

The standard deviation of a count rate is

where sis the standard deviation of the total countn of a radioactive
sample obtained in time t. Becausen is equal to the count rate ctimes the
counting time t,

(4.3)

Problem 4.2
A radioactive sample is counted for 12 min and gives 8640 counts. Calcu-
late the count rate and its standard deviation for the sample.

Answer

Standard deviation,

Therefore, the count rate is 720 ±8 cpm.

Propagation of Errors

Situations arise in which two quantities, say xand y, with their respective
standard deviations,sxand sy, are either added, subtracted, multiplied, or
divided. The standard deviations of the results of these arithmetic opera-
tions are given by the following expressions:

Addition:

(4.4)

Subtraction:

(4.5)

Multiplication:

(4.6)

Division:

sss()xy=()( )xy xx+()yy (4.7)

22

sss()xy× =×()( )xy xx+()yy

22

sssxy− =+x^22 y

sssxy+ =+x^22 y

sc==ct 720 12≈ 8

Count rate c== counts per minute cpm()

8640

12

720

sc n t ct t

c

t

== =

s

s

c

t

=

Propagation of Errors 37