Answer
$R = 6.92 \times 10^7 /h = 7.0 \times 10^7 /h$
In one hour, $7.0 \times 10^7 $ electrons will intercept.
Work Step by Step
Assuming target area is $1 \space m^2$
$\frac{Target \space rate}{Total \space rate \space upward} = \frac{1 \space m^2}{(2.6 \times 10^5 km^2) (1000 m/km^2)} = 3.846 \times 10^{-12}$
Half beta decay
$R= \frac{1}{2} (1 \times 10^{16} /s ) ( 3.846 \times 10^{-12}) = 19230 /s$
To know the rate of decay at one hour, convert R to hour
$R = (19230 /s)(3600 s/h) = 6.92 \times 10^7 /h$
$R = 7.0 \times 10^7 /h$
So in one hour, $7.0 \times 10^7 $ electrons will intercept.
