62. The Hydrogen Maser. 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 $1 \sin 100,000$ 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 \mathrm{~h} $? (c) How many cycles would have occurred during the age of the earth, which is estimated to be $4.6 \times 10^{9}$ years? (d) By how many seconds would a hydrogen maser clock be off after a time interval equal to the age of the earth?
