Question

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 ss in 100,000 years. (The large number of significant figures given for the frequency simply illustrates the remarkable accuracy to which it has been measured.)

PART A

What is the time for one cycle of the radio wave?

Express your answer to three significant figures and include the appropriate units.

PART B

How many cycles occur in 1.9 hh?

PART C

How many cycles would have occurred during the age of the earth, which is estimated to be 4.6×1094.6×109 years?

PART D

By how many seconds would a hydrogen maser clock be off after a time interval equal to the age of the earth?

Express your answer in seconds.

Answer 1

The frequency of these waves, f = 1,420,405,751.786 Hz

PART A

Time for one cycle, T = 1/f = 1/1,420,405,751.786 = 7.04 x 10-10 s

Time for one cycle, T = 7.04 x 10-10 s

PART B

Total time = number of cycles x time for one cycle

t = nT

Number of cycles, n = t/T

Given: t = 1.9 hour = 1.9 x 3600 s = 6840 s

n = t/T = 6840/ 7.04 x 10-10= 9.71 x 1012 cycles

number of cycles occur, n = 9.71 x 1012 cycles

PART C

age of the earth, t = 4.6×1094.6×109 years = 1.59 x 1020 s

Total time = number of cycles x time for one cycle

t = nT

Number of cycles, n = t/T

n = t/T = 1.59 x 1020 /7.04 x 10-10 = 2.25 x 1029 cycles

number of cycles occur, n = 2.25 x 1029 cycles

PART D

A clock controlled by a hydrogen maser is off by only 1 s in 100,000 years

Number of seconds would a hydrogen maser clock be off after a time interval equal to the age of the earth, n = age of earth/ 100000 = 4.6×1094.6×109 /100000 = 5.03 x 107 s