Which of the following statements are true regarding the electromagnetic spectrum? 1. x rays and gamma rays have very long wavelengths and very low photon energies.2. radio waves have wavelengths on the order of meters and very low photon energies.3. ultraviolet radiation has long wavelengths and low photon energies.4. visible light lies at the center of the electromagnetic spectrum.5. infrared radiation has long wavelengths and low photon energies.

2, 4, 5

Explanation:

The electromagnetic spectrum gives the classification of the electromagnetic waves according to their wavelength/frequency. In order from the shortest to the greatest wavelength, we have:

Gamma rays

X-rays

Ultraviolet

Visible light

Infrared

Microwaves

Radio waves

Moreover, the frequency of an electromagnetic wave is inversely proportional to its wavelength, according to:

where c is the speed of light.

Finally, the energy of a photon of an electromagnetic wave is directly proportional to the frequency, and inversely proportional to the wavelength:

where h is the Planck constant.

Keeping in mind these facts, let's now analyze each statement:

1. X rays and gamma rays have very long wavelengths and very low photon energies. --> FALSE: X-rays and gamma rays have the shortest wavelength, so they have the highest frequency and very high energy.

2. Radio waves have wavelengths on the order of meters and very low photon energies. --> TRUE. Radio wave wavelengths are on the order of meters, so very long; consequently, their frequency is very low, and so their energy is also very low.

3. Ultraviolet radiation has long wavelengths and low photon energies. --> FALSE. Ultraviolet has short wavelength, so high frequency and high photon energy.

4. Visible light lies at the center of the electromagnetic spectrum. --> TRUE: visible light photons have wavelength between 380 and 750 nm, and lie at the center of the electromagnetic spectrum.

5. Infrared radiation has long wavelengths and low photon energies. --> TRUE: infrared radiation has longer wavelengths (if compared to the visible light), and therefore lower frequency and lower energy.

pythagoras' theorem

square root (-5^2+9^2)

square root (25+81)

square root (106)

angle is tan^-1(9/5)

neg x, pos y