A diagnostic medical device emits electromagnetic radiation with a frequency of 6.0 \times… — JAMB UTME

A diagnostic medical device emits electromagnetic radiation with a frequency of $6.0 \times 10^{18}\text{ Hz}$ in a vacuum. Given that the speed of light in a vacuum is $c = 3.0 \times 10^8\text{ m/s}$ , what is the wavelength of this radiation, and to which part of the electromagnetic spectrum does it belong?

$5.0 \times 10^{-11}\text{ m}$ , X-raysAnswer
B
$5.0 \times 10^{-11}\text{ m}$ , Ultraviolet rays
C
$2.0 \times 10^{10}\text{ m}$ , X-rays
D
$1.8 \times 10^{27}\text{ m}$ , Gamma rays

Answer

The wavelength of the radiation is

5.0 \times 10^{-11}\text{ m}

, which corresponds to X-rays.

Using the wave equation

\lambda = \frac{c}{f}

, dividing

3.0 \times 10^8\text{ m/s}

6.0 \times 10^{18}\text{ Hz}

yields

\lambda = 5.0 \times 10^{-11}\text{ m}

. Radiation with a wavelength of

5.0 \times 10^{-11}\text{ m}

(frequency

6.0 \times 10^{18}\text{ Hz}

) falls in the X-ray portion of the electromagnetic spectrum.

Step-by-Step Solution

Identify the given values and the wave equation relating speed, frequency, and wavelength.

Speed of light

c = 3.0 \times 10^8\text{ m/s}

, frequency

f = 6.0 \times 10^{18}\text{ Hz}

. Equation:

c = f \lambda \implies \lambda = \frac{c}{f}

Electromagnetic waves propagate in a vacuum at speed

c

Calculate the wavelength

\lambda

\lambda = \frac{3.0 \times 10^8\text{ m/s}}{6.0 \times 10^{18}\text{ s}^{-1}} = 0.5 \times 10^{-10}\text{ m} = 5.0 \times 10^{-11}\text{ m}.

Proper division of scientific notation terms.

Classify the electromagnetic spectral region based on the calculated wavelength.

Wavelengths in the range

10^{-11}\text{ m}

10^{-8}\text{ m}

correspond to X-rays.

X-rays typically span frequencies between

3 \times 10^{16}\text{ Hz}

and

3 \times 10^{19}\text{ Hz}

Key Concept

Wave equation for electromagnetic waves and spectral region identification

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