A certain radio wave has a wavelength of 8 × 10^-2 m, and a certain gamma ray has a wavelength of 2 × 10^-12 m. Which of the following is true?

Question

A.
The wavelength of the radio wave is forty billion times the wavelength of the gamma ray.

B.
The wavelength of the gamma ray is forty billion times the wavelength of the radio wave.

C.
The wavelength of the gamma ray is four billion times the wavelength of the radio wave.

D.
The wavelength of the radio wave is four billion times the wavelength of the gamma ray.

Answer 1

To determine the relationship between the wavelengths of the radio wave and the gamma ray, we will compare their wavelengths directly.

The wavelength of the radio wave is given as: \[ \text{Wavelength of radio wave} = 8 \times 10^{-2} \text{ m} \]

The wavelength of the gamma ray is given as: \[ \text{Wavelength of gamma ray} = 2 \times 10^{-12} \text{ m} \]

Next, let's calculate how many times the wavelength of the radio wave is compared to the wavelength of the gamma ray:

\[ \frac{\text{Wavelength of radio wave}}{\text{Wavelength of gamma ray}} = \frac{8 \times 10^{-2}}{2 \times 10^{-12}} \]

Now, simplifying the fraction:

\[ = \frac{8}{2} \times \frac{10^{-2}}{10^{-12}} \] \[ = 4 \times 10^{10} \]

This tells us that the wavelength of the radio wave is \(4 \times 10^{10}\) times the wavelength of the gamma ray.

Now, evaluating the options:

A. The wavelength of the radio wave is forty billion times the wavelength of the gamma ray. (True, as \(4 \times 10^{10}\) is indeed forty billion.)

B. The wavelength of the gamma ray is forty billion times the wavelength of the radio wave. (False.)

C. The wavelength of the gamma ray is four billion times the wavelength of the radio wave. (False.)

D. The wavelength of the radio wave is four billion times the wavelength of the gamma ray. (False, as it is forty billion times.)

Thus, the correct answer is:

A. The wavelength of the radio wave is forty billion times the wavelength of the gamma ray.