Question

Electromagnetic waves are traveling in the vacuum of space. Calculate the wavelengths of these electromagnetic waves with the following frequencies. (Enter the first wavelength in pm and the second wavelength in cm.)

(a) 2.00 x 1019 Hz
(b) 4.50 x109 Hz

Answer 1

(a) 1.5×10⁻¹¹ m.

(b) 6.7×10⁻² m

Step-by-step explanation:

Note: All Electromagnetic wave travels in with the same speed, which 3×10⁸ m/s

(a) Give a frequency of 2.00×10¹⁹ Hz.

Using the equation of a wave,

V = λf................ Equation 1

Where V = Speed of electromagnetic wave, λ = wavelength, f = frequency.

make λ the subject of the equation

λ = V/f................. Equation 2

Given: f = 2.00×10¹⁹ Hz.

Constant: v = 3×10⁸ m/s.

Substitute into equation 2

λ = 3×10⁸/2.00×10¹⁹

λ = 1.5×10⁻¹¹ m.

(b) Similarly using

λ = v/f

Given: f = 4.5×10⁹ Hz, and v = 3×10⁸ m/s.

Substitute these values into equation 2 above.

λ = 3×10⁸/4.5×10⁹

λ = 6.7×10⁻² m