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Question
It is claimed that two cesium clocks, if allowed to run for 100 years, free from any disturbance, may differ by only about 0.02 s. What does this imply for the accuracy of the standard cesium clock in measuring a time-interval of 1 s?
Solution 1
Difference in time of caesium clocks = 0.02 s
Time required for this difference = 100 years
= 100 × 365 × 24 × 60 × 60 = 3.15 × 109 s
In 3.15 × 109 s, the caesium clock shows a time difference of 0.02 s.
In 1s, the clock will show a time difference of `0.02/(3.15 xx 10^(9)) s`
Hence, the accuracy of a standard caesium clock in measuring a time interval of 1 s is
`(3.15 xx 10^9)/0.02 = 157.5 10^9s ~~ 1.5 xx 10^11 s`
Solution 2
Total time = 100 years = 100 x 365 x 24 x 60 x 60 s
Error in 1 second=0.02/100 x 365 x 24 x 60 x 60
=6.34 x 10-12 s
∴Accuracy of 1 part in 1011 to 1012.
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