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 ?
Given: 100 years are required to show the difference of 0.02 seconds.
Convert years into seconds,
Time in seconds = 100 × 365 × 24 × 60 × 60 = 3.15 × 10 9 sec
Fractional error = Difference in time ( s ) Time intervel ( s )
Cesium clock shows the difference of 0.02 sec in 3.15 × 10 9 sec,
Then in 1 sec the clock shows difference of 0.02 3.15 × 10 9 sec .
0.02 3.15 × 10 9 sec = 6.35 × 10 − 10 sec = 10 − 11 sec
Therefore, in 1s the difference is 10 − 11 .
Degree of Accuracy = 1 10 − 11 = 10 11
Thus, the degree of accuracy shown by the cesium clock in 1s is from 10 11 .
Given: 100 years are required to show the difference of 0.02 seconds.
Convert years into seconds,
Fractional error
Cesium clock shows the difference of 0.02 sec in
Then in 1 sec the clock shows difference of
Therefore, in 1s the difference is
Thus, the degree of accuracy shown by the cesium clock in 1s is from
