Question

To understand electromagnetic radiation and be able to perform calculations involving wavelength, frequency, and energy. Several properties are used to define waves. Every wave has a wavelength, which is the distance from peak to peak or trough to trough. Wavelength, typically given the symbol λ (lowercase Greek "lambda"), is usually measured in meters. Every wave also has a frequency, which is the number of wavelengths that pass a certain point during a given period of time. Frequency, given the symbol ν (lowercase Greek "nu"), is usually measured in inverse seconds (s−1). Hertz (Hz), another unit of frequency, is equivalent to inverse seconds. The product of wavelength and frequency is the speed in meters per second (m/s). For light waves, the speed is constant. The speed of light is symbolized by the letter c and is always equal to 2.998×108 m/s in a vacuum; that is, c=λν=2.998×108m/s Another term for "light" is electromagnetic radiation, which encompasses not only visible light but also gamma rays, X-rays, UV rays, infrared rays, microwaves, and radio waves. As you could probably guess, these different kinds of radiation are associated with different energy regimes. Gamma rays have the greatest energy, whereas radio waves have the least energy. The energy (measured in joules) of a photon for a particular kind of light wave is equal to its frequency times a constant called Planck's constant, symbolized h: Ephoton=hν where h=6.626×10−34J⋅s These two equations can be combined to give an equation that relates energy to wavelength: E=hcλ

Part A A radio station's channel, such as 100.7 FM or 92.3 FM, is actually its frequency in megahertz (MHz), where 1MHz=106Hz and 1Hz=1s−1. Calculate the broadcast wavelength of the radio station 102.9 FM. Express your answer to four significant figures and include the appropriate units. Part B Green light has a frequency of about 6.00×1014s−1. What is the energy of a photon of green light? Express your answer to three significant figures and include the appropriate units. Part C Hospital X-ray generators emit X-rays with wavelength of about 15.0 nanometers (nm), where 1nm=10−9m. What is the energy of a photon of the X-rays? Express your answer to three significant figures and include the appropriate units.

Answer 1

A)

Given:

f = 1.029*10^8 s-1

use:

lambda = c/f

=(3.0*10^8 m/s)/(1.029*10^8 s-1)

= 2.915 m

Answer: 2.915 m

B)

Given:

f = 6*10^14 s-1

use:

E = h*f

=(6.626*10^-34 J.s)*(6*10^14) s-1

= 3.976*10^-19 J

Answer: 3.98*10^-19 J

C)

Given:

lambda = 1.5*10^-8 m

use:

E = h*c/lambda

=(6.626*10^-34 J.s)*(3.0*10^8 m/s)/(1.5*10^-8 m)

= 1.325*10^-17 J

Answer: 1.33*10^-17 J