A radioactive source emits X–rays of very short wavelength (10$^{-13}$m ). What is the frequency of these rays?

1. Analyze the question

We are given the wavelength ($\lambda$) of X-rays and asked to calculate the frequency ($f$). We know that X-rays are electromagnetic waves, which means they travel at the speed of light ($c$).

2. Explain the concept

The relationship between the speed of a wave, its frequency, and its wavelength is given by the wave equation:

Where:

• $c$ is the speed of light in a vacuum, approximately $3.0 \times 10^8 \text{ m/s}$.
• $f$ is the frequency in Hertz (Hz).
• $\lambda$ (lambda) is the wavelength in meters (m).

To find the frequency, we rearrange the formula:

3. Show the solution

Given:

• $c = 3.0 \times 10^8 \text{ m/s}$
• $\lambda = 10^{-13} \text{ m}$

Calculation:

Using the laws of indices, when you divide powers of the same base, you subtract the exponents:

4. Identify the answer

Comparing our result to the given options: A. $2 \times 10^{18} \text{ Hz}$ B. $3 \times 10^{19} \text{ Hz}$ C. $3 \times 10^{21} \text{ Hz}$ D. $3 \times 10^{-19} \text{ Hz}$

The calculated value matches option C.

5. Tip

When dealing with electromagnetic wave problems in JAMB, always remember that the speed of light ($c = 3 \times 10^8 \text{ m/s}$) is a constant you are expected to know. Also, pay close attention to the laws of indices—a common mistake is to accidentally add the exponents instead of subtracting them when dividing, or getting the sign wrong when subtracting a negative number!