Answer
(a) $7.04\times 10^{-10}~s$
(b) $5.11\times 10^{12}~cycles$
(c) $2.06\times 10^{26}~cycles$
(d) $4.6\times 10^4$ seconds
Work Step by Step
$f = 1.42\times 10^9~Hz$
(a) The time for one cycle is 1/f.
$1/f = (1/1.42) \times 10^{-9} ~s = 7.04\times 10^{-10}~s$
(b) We can find the number of cycles in one hour (which is 3600 seconds).
$(1.42\times 10^9~Hz)(3600~s) = 5.11\times 10^{12}~cycles$
(c) We can find the number of cycles in $4.6\times 10^9~years$.
$(1.42\times 10^9~Hz)(3600~s/hr)(24~hr/day)(365~days/year)(4.6\times 10^9~years)$
$= 2.06\times 10^{26}~cycles$
(d) $\frac{4.6\times 10^9~years}{10^5~years} = 4.6\times 10^4$
Since the clock is off by 1 second every 100,000 years, the clock would be off by $4.6\times 10^4$ seconds in a time interval equal to the age of the Earth.
