The Hydrogen Maser. A maser is a laser-type device that produces electromagnetic waves with frequencies in the microwave and radio-wave bands of the electromagnetic spectrum. You can use the radio waves generated by a hydrogen maser as a standard of frequency. The frequency of these waves is 1,420,405,751.786 hertz. (A hertz is another name for one cycle per second.) A clock controlled by a hydrogen maser is off by only 1 s in 100,000 years. For the following questions, use only three significant figures. (The large number of significant figures given for the frequency simply illustrates the remarkable accuracy to which it has been measured.) (a) What is the time for one cycle of the radio wave? (b) How many cycles occur in 1 h? (c) How many cycles would have occurred during the age of the earth, which is estimated to be 4.6 X 109 years? (d) By how many seconds would a hydrogen maser clock be off after a time interval equal to the age of the earth?
Solution 56P Given The frequency of radio waves = 1,420,405,751.786 hertz Case (1) We need find the time taken for 1 cycle by radio wave This is obtained as 1420405751.786 7.040241841 × 10 7 Hence time taken for 1 second is 7.040241841 × 10 7 Case (2) We need to find the number cycles in 1 hr Finding the time in terms of seconds 1hr = 60s × 60s = 3600s Number of cycles is 3600s × 1,420,405,751.786 hertz 12 = 5.113460704 × 10 12 Hence the number of cycles in one hour is = 5.113460704 × 10 Case (3) We need to find number of cycles for earth’s age which is 4.6 × 109 years Let us find number of seconds in a year 60sec × 60min × 24hour × 365days = 31536000 s /year Now we need find for 4.6 × 109 years This is obtained as 31536000 s /year × 4.6 × 10 years = 1.450656 × 10 17 9 Hence the number of cycles for earth age 4.6 × 10 years is obtained as 17 1.450656 × 10 Case (4) We need find number seconds would a hydrogen maser clock be off after a time interval of earth age It is given the hydrogen maser turns off for 1 s after 100,000 year The earth age is given 9 4.6 × 10 years Hence the time interval is 4.6×10 years 100000 = 46000 times 9 Hence the time interval for 4.6 × 10 yearsis 46000 times